Calculus I

Math 2413: Calculus I

Go here for a prerequisite review sheet for Calculus. If you can work about 80% of these problems correctly, you will probably be okay for Calculus.

Go here for any extra homework assignment(s) I mention in class.

Spring 2019

Synonym: 71945, Section: 006, Northridge 2244
Tuesday / Thursday 2:00 pm - 3:45 pm

Course Content:

Course Description: MATH 2413 CALCULUS I (4-4-0) A standard first course in calculus. Topics include inequalities; functions; limits; continuity; the derivative; differentiation of algebraic functions and trigonometric functions; Newton's method; applications of the derivative; the integral; integration of algebraic functions and the sine and cosine functions; numerical integration; and applications of the integral.  Instructional Methodology: This course is taught in the classroom primarily as a lecture/discussion.Course Rationale: This course is the first course in the traditional calculus sequence for mathematics, science and engineering students. It is part of what could be a four-semester sequence in calculus courses. The approach allows the use of technology and the rule of four (topics are presented geometrically, numerically, algebraically, and verbally) to focus on conceptual understanding. At the same time, it retains the strength of the traditional calculus by exposing the students to the rigor of proofs and the full variety of traditional topics: limits, continuity, derivative, applications of the derivative, and an introduction to the definite integral.


Please make sure you have the necessary prerequisites for this course: Satisfactory scores on both the ACC Mathematics Assessment and Higher Level Placement Tests OR departmental approval.


You should bring your homework to class every day.  It will be collected regularly.  There will also be in-class assignments or quizzes collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than a week late might not receive any credit.  If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.

Course Materials:

Text: Calculus: Concepts and Contexts, 4th ed., by James Stewart, Brooks/Cole 2010

Please Note: For Calculus I and Calculus II, the Single Version (SV) is required. ISBN 9781111027308  For Calculus III, the Multivariable Version (MV) is required. ISBN 9780538460293 You can purchase a Full Version of the text that includes all material for Calculus I, II, and III if you plan to take the entire sequence at Austin Community College.  ISBN 9780538796859



Online Component:  Enhanced WebAssign (EWA) may be required for one or all of the Calculus courses.  (It will not be required for this class.) Access to EWA includes a complete online eBook.  You may purchase EWA access in one of three ways: 

· Bundled textbooks with access codes are available at ACC bookstores.

· Bundled textbooks with access codes are available for purchase and delivery from the publisher.

· You may use a credit card or PayPal to purchase EWA access online with the online book if you do not want a hardcover book from the website above. 

It is recommended that you register for EWA when you purchase your textbook regardless of whether or not your initial instructor requires the program. Please refer to the handout for login and enrollment information.

Student Solutions Manual, ISBN 9780495560616, by Jeffrey A. Cole


You must have access to technology that enables you to (1) Graph a function, (2) Find the zeroes of a function. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use. Other calculator brands can also be used. Your instructor will determine the extent of calculator use in your class section.                 


There will be 3 exams plus a final exam (part of which will be comprehensive). Grades will be weighted as follows:


Tests 1, 2, 3




Final Exam







Sometime after Test 3, there will be a single make-up exam over the material on tests 1-3; the grade on this exam can be used to replace your lowest grade on the first three tests, up to a maximum grade of 85 if you make complete corrections for tests 1-3 or 70 without the completed corrections.

If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class.  If you miss a test, you must try to take it during this “late” period.  If you do not take the test during that period, you will receive a 0 for that grade.  In that case, you will need to take the make-up exam to replace that 0. 

Grades will be assigned as follows:

A :

90% or better and a grade of at least 80% on the final

D :

60% - 69%

B :

80% - 89% and a grade of at least 70% on the final

F :

below 60%

C :

70% - 79% and a grade of at least 60% on the final




W :

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I :

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


Attendance is required in this course.  It is extremely important for you to attend class regularly.  I MAY drop you from the course for excessive absences, although I make no commitment to do so.


It is the student's responsibility to initiate all withdrawals in this course.  The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.

Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.

The withdrawal deadline for Spring 2019 is April 29, 2019.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Classroom behavior:

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook on the web at:

Class participation:


All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Time required and outside help:

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:



Course Objectives for MATH 2413:


1.   Find limits of functions (graphically, numerically and algebraically)

2.   Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.

3.   Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation. Use these derivatives to study the characteristics of curves. Determine derivatives using implicit differentiation and use to study characteristics of a curve.

4.   Construct detailed graphs of nontrivial functions using derivatives and limits.

5.   Use basic techniques of integration to find particular or general antiderivatives.

6.   Demonstrate the connection between area and the definite integral.

7.   Apply the Fundamental theorem of calculus to evaluate definite integrals.

8.   Use differentiation and integration to solve real world problems such as rate of change, optimization, and area problems.


Student Learning Outcomes for MATH 2413:


Upon successful completion of this course, students will:


1.   Solve tangent and area problems using the concepts of limits, derivatives, and integrals.

2.   Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.

3.   Determine whether a function is continuous and/or differentiable at a point using limits.

4.   Use differentiation rules to differentiate algebraic and transcendental functions.

5.   Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.

6.   Evaluate definite integrals using the Fundamental Theorem of Calculus.

7.   Demonstrate an understanding of the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.


The General Education Competency of:

1.   Critical Thinking: gathering, analyzing, synthesizing, evaluating and applying information is covered in every SLO.

2.   Quantitative and Empirical Reasoning: applying mathematical, logical, and scientific principles and methods is covered in every SLO.

3.   Technology Skills: using appropriate technology to retrieve, manage, analyze, and present information is covered in SLOs # 1, 2, 3, 5, and 7.

4.   Written, Oral and Visual Communication: communicating effectively adapting to purpose, structure, audience and medium is covered in every SLO.


ACC College Policies

Statement on Scholastic Dishonesty - A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at


Student Rights and Responsibilities - Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.


Statement on Students with Disabilities - Each ACC campus offers support services for students with documented disabilities. Students with disabilities who need classroom, academic or other accommodations must request them through Student Accessibility Services (SAS, formerly OSD).  Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.


Students who have received approval for accommodations from SAS for this course must provide the instructor with the ‘Notice of Approved Accommodations’ from SAS before accommodations will be provided.  Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodations’ from the student.


Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodations’ to the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.  Additional information about Student Accessibility Services is available at  HYPERLINK ""


Safety Statement - Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at


Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.


You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.


Communication with your Instructor - All e-mail communication to students will be sent solely to the student’s ACCmail account or math software if applicable, with the expectation that such communications will be read in a timely fashion.  Likewise, students should use their ACCmail account or math software when communicating with instructors.  Instructors will respond to student emails within 3 business days, if no response has been received by the student at the end of that time, then the student should send a reminder to the instructor.


Testing Center Policy - Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:


·    ACC Photo ID

·    Course Abbreviation (e.g., ENGL)

·    Course Number (e.g.,1301)

·    Course Synonym (e.g., 10123)

·    Course Section (e.g., 005)

·    Instructor's Name

Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at


Student And Instructional Services - ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at: Links to many student services and other information can be found at: For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.


Concealed Handgun Policy - The Austin Community College District concealed handgun policy ensures compliance with Section 411.2031 of the Texas Government Code (also known as the Campus Carry Law), while maintaining ACC’s commitment to provide a safe environment for its students, faculty, staff, and visitors. Beginning August 1, 2017, individuals who are licensed to carry (LTC) may do so on campus premises except in locations and at activities prohibited by state or federal law, or the college’s concealed handgun policy. It is the responsibility of license holders to conceal their handguns at all times. Persons who see a handgun on campus are asked to contact the ACC Police Department by dialing 222 from a campus phone or 512-223-7999. Refer to the concealed handgun policy online at


Student Support Services - Resources to support you are available at every campus.  Food pantries are available at all campus Student Life offices (  Assistance paying for childcare or utility bills is available at any campus Support Center (  For sudden, unexpected expenses that may cause you to withdraw from one or more of your courses, go to to request emergency assistance through the Student Emergency Fund.  Help with budgeting for college and family life is available through the Student Money Management Office (  Counselors are available at any campus if you experience a personal or mental health concern (  All services are free and confidential.


Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.







1.1 - 1.3

Review of functions and transformations



1.4 - 1.7

Graphing technology, review of exponential, inverse, and logarithmic functions, and parametric curves



2.1, 2.2, 2.3

Velocity and the tangent line, the idea of the limit; calculating limits



2.3, 2.4, 2.5

More calculation of limits, Continuity, Limits and infinity




The derivative and the rate of change



2.6 - 2.7

More on the derivative and considering the derivative as a function




Graphing the derivative and review for Test 1



Test 1 (in class)




What the derivative tells us about the original function




Derivatives of polynomial and exponential functions



3.2 - 3.3

The product rule and quotient rule and derivatives of trigonometric functions




The chain rule



3.5, 3.7

Implicit differentiation and derivatives of logarithmic functions




Related rates



3.6, 3.9

Derivatives of inverse trig functions, linear approximations and differentials




More on differentials and review for Test 2


Test 2 – Dates to be announced in class (probably in the Testing Center)

March 18 - 24, 2019 - Spring Break




Maximum and minimum values of a function




Derivatives and the shape of




More on graphing and when to reach for a graphing calculator/computer




Indeterminate forms and L’Hopital’s Rule




Optimization problems




More optimization problems




Newton’s Method




Rates of change in the natural and social sciences


Test 3 – Dates to be announced in class (probably in the Testing Center)




The antiderivative



5.1 - 5.2

Areas, distances, and the definite integral




Evaluating the definite integral




Solving integrals via substitution




More substitution



5.4, 5.5

The Fundamental Theorem of Calculus (and more substitution)



Final Exam, Part 1



Final Exam, Part 2




This webpage was created by Marcus McGuff.
It was last updated on January 12, 2019 .