in Math articles

Calculus 1

1. Syllabus(pdf)

  • Textbook

Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart.(ISBN: 978-1-305-27033-6)

  • About the Course

Mathematics 1201 is an introduction to calculus: limits and continuity; derivatives and integrals of algebraic, exponential, logarithmic, and trigonometric functions of one variable; methods of numerical approximation, and applications of the derivative to mathematics, physics, engineering, biology, chemistry, and other fields.

We will cover Chapters 1 to 5 of the textbook. In this course you will learn a number of useful formulas, though their mastery is not the primary purpose of calculus any more than correct spelling is the primary purpose of literature. Our goal is to have you learn how to understand calculus conceptually so you can build your own approaches to solving practical problems.

  • Grades

The total grade will be calculated based on the following weighting:

Three Midterm Exams (20% each), In-class Projects(10%), Final Exam (30%)

If your final exam score is higher than your lowest exam score, the former will replace the latter. Once the total grade is calculated, the letter grade will be assigned following the standard scale. You will be graded on an absolute scale, NOT graded on a curve.

  • Project

You will work on in-class projects in small groups with your classmates every week. I, the instructor, will facilitate your work on the projects, but the goal is for you (and your group-mates) to work through, and complete these projects on your own as much as possible.

  • Worksheet

The purpose of in-class worksheets is the same as in-class projects, but the worksheets are not graded.

  • Homework

You will be assigned exercise problems out of the textbook in each class. You are not required, but highly encouraged to work on these problems and submit a write-up. I will provide a full feedback for your submitted work. You may work together on homework to understand and solve the problems, but writing up the solution should be done independently.

2. Course Schedule(pdf)

Week

Monday

Wednesday

1

2.1 Tangent, Velocity Problem 2.2 Limit of a function

Project 1 / Solution

2

2.3 Calculating Limits using the Limit Laws

Worksheet 1 / Solution

2.5 Continuity

Project 2 / Solution

3

Break

2.6 Limits at Infinity

Project 3 / Solution

4

Break

2.7 Derivatives and Rates of Change

Project 4 / Solution

5

2.8 The Derivative as a Function

Worksheet 2 / Solution

Exam 1

Exam 1 / Solution

6

3.1 Derivatives of polynomial and exponential functions

3.2 Product and Quotient Rules

Worksheet 3 / Solution

3.3 Derivative of trig functions

Project 5 / Solution

7

3.4 Chain Rule

Project 6 / Solution

3.6 Derivative of logarithmic functions

Worksheet 4 / Solution

8

3.9 Related Rates

Project 7

3.10 Linear approximation

Worksheet 5 / Solution

9

Exam 2

Exam 2 / Solution

4.1 Maximum and Minimum

Worksheet 6 / Solution

10

4.2 Mean Value Theorem 4.3 Derivatives and Shapes

Project 8 / Solution

11

Break

12

4.5 Curve Sketching

Project 9 / Solution

13

4.7 Optimization Problems

Worksheet 8

4.9 Antiderivatives

Project 10 / Solution

14

5.1 Areas and Distances

Worksheet 9 / Solution

Exam 3

Exam 3 / Solution

15

5.2 Definite Integral

Worksheet 10 / Solution

5.3 Fundamental Theorem of Calculus

Worksheet 11 / Solution

16

5.4 Indefinite Integrals and Net Change 5.5 The Substitution Rule

Worksheet 12 / Solution

17

Final

 

3. Other Course Document

1) Chapter 4 Checklist(pdf)

2) Chapter 4 Finding Absolute Extrema(pdf)

4. Homework(pdf)