## Math 220. Calculus

Lecture Syllabus

**Textbook: Stewart, Calculus: Early Transcendentals,
8th edition, with Enhanced Webassign**,

**Thomson Brooks/Cole**.

This syllabus assumes MWF lectures and Tuesday-Thursday discussion sections, with 43 lecture hours in the semester. It includes 36 lectures, leaving 7 hours for leeway and exams. Note that a minimum of 4 one-hour exams is recommended for Math 220, but one can give 5 if there is time.

Math 220 is intended for students who have NOT had a year of calculus in high school.

This is primarily a course on calculation and problem solving; proofs should not be emphasized. Chapter 1 is optional since it represents review material. Instructors may choose to eliminate it or cover it at a pace more rapid than that suggested by the 4 lecture provision. However, many Math 220 students do need review of this material.

It is assumed that the Teaching Assistants in this course may need to do some lecturing in their discussion sections so as to keep the timeline for the syllabus on track.

### Chapter 1: Functions and Models (4 lectures)

1.1 Four Ways to Represent a Function

1.2 Mathematical Models: A Catalog of Essential Functions

1.3 New Functions from Old Functions

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

### Chapter 2: Limits and Derivatives (5 lectures)

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit (optional)

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change

2.8 The Derivative as a Function

### Chapter 3: Differentiation Rules (8 lectures)

3.1 Derivatives of Polynomials and Exponential Functions

3.2 The Product and Quotient Rules

3.3 Derivatives of the Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Natural and Social Sciences

3.8 Exponential Growth and Decay

3.9 Related Rates

3.10 Linear Approximations and Differentials

3.11 Hyperbolic Functions

### Chapter 4: Applications of Differentiation (7 lectures)

4.1 Maximum and Minimum Values

4.2 Mean Value Theorem

4.3 How Derivatives Affect the Shape of a Graph

4.4 Indeterminate Forms and L'Hospital's Rule

4.5 Summary of Curve Sketching

4.7 Optimization Problems

4.8 Newton's Method

4.9 Antiderivatives

### Chapter 5: Integrals (7 lectures)

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 The Substitution Rule

### Chapter 6: Applications of Integration (5 lectures)

6.1 Areas Between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.4 Work

6.5 Average Value of a Function

**Course Prerequisite:** An adequate ALEKS placement score as described at http://math.illinois.edu/ALEKS/, demonstrating knowledge of topics of MATH 115. Students who take Math 115 to prepare for Math 220 are recommended to have a C or higher as well as the required ALEKS score.

Revised 10/26/17