MAT 1500 Calculus I

Syllabus

Textbook: Stewart: Calculus: Early Trancendentals, 7th Edition, Brooks/Cole, 2012
Coordinators: Marilyn Belkin and Joyce Longman

Chapter 1: Functions and Models
1.1 Four ways to Represent a Function
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms

Chapter 2. Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
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
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of 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 Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates

4. Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivatives and the Shapes Of Curves
4.4 Indeterminate Forms and L'Hopital's Rule
4.5 Summary of Curve Sketching
4.6 Graphing with Calculus and Calculators
4.7 Optimization Problems

Chapter 5:  Integrals

5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals & Net Change Theorem
5.5 The Substitution Rule

A suggested schedule based on a 14 week (56 class hours) semester, is given below. It may be modified at the instructor's discretion.

Sections                         Approximate Time            Comments

Algebra & Trig Review            2 class hours                   Use Appendix  A, B, D
1.1, 1.5, 1.6                         3 class hours
2.1-2.9                                 9 class hours          
3.1-3.9                                 12 class hours 
4.1-4.9                                 10 class hours

5.1-5.5                                 9 Class hours

Chapter Reviews                    4 class hours               Reviews appear at the end of each chapter,

                                                                            refer to heading below

Exam Reviews                       4 class hours                  Includes Final Exam Review

Exams                                  3 class hours

Maple or other computer software

Maple or other computer software discussions should be determined by each instructor. Each student should master the following topics:

(1) assigning variables, expressions, and functions, (2) evaluating expressions and functions, (3) distinctions between exact and approximate arithmetic, (4) graphing, (5) using graphs to solve equations exactly and approximately, (6) finding limits (numerical and exact) and derivatives, and (7) knowing how to use the "help" command.