Textbook: Stewart, Calculus - Early Transcendentals, 4th Edition, Brooks/Cole

1999

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1. MATH-1610 COURSE OUTLINE

Chapter 1..................................................................2

1.5 & 1.6 Review of Functions and Inverse Functions, Exponentials and

Logarithms----------------------------------------------------------------2

Chapter 2..................................................................10

2.1 The Tangent and Velocity Problems-------------------------------------1

2.2 & 2.3 The Limit of a Function-----------------------------------------3

2.5 Continuity------------------------------------------------------------1

2.6 Limits at Infinity and Horizontal Asymptotes--------------------------2

2.7, 2.8 & 2.9 Definition of the Derivative-------------------------------3

Chapter 3..................................................................20

3.1 Derivatives of Polynomials and Exponential Functions------------------1

3.2 The Product and Quotient Rules----------------------------------------2

3.3 Rates of Change in the Natural and Social Sciences--------------------1

3.4 Derivatives of Trigonometric Functions--------------------------------2

3.5 The Chain Rule--------------------------------------------------------3

3.6 Implicit Differentiation (Inverse Trigonometric Functions)------------4

3.7 Higher Derivatives----------------------------------------------------1

3.8 Derivatives of Logarithmic Functions----------------------------------2

3.10 Related Rates--------------------------------------------------------2

3.11 Linear Approximations and Differentials------------------------------2

Chapter 4..................................................................11

4.1 & 4.2 Maximum/Minimum Values and the Mean Value Theorem---------------2

4.4 Indeterminate Forms and L'Hospital's Rule-----------------------------3

4.3, 4.5 & 4.6 Curve Sketching--------------------------------------------3

4.7 Optimization Problems-------------------------------------------------2

4.10 Antiderivatives------------------------------------------------------1

Chapter 5..................................................................10

Appendix E Sigma Notation-------------------------------------------------1

5.1 Areas and Distances---------------------------------------------------2

5.2 Definite Integrals----------------------------------------------------2

5.3 The Fundamental Theorem of Calculus-----------------------------------2

5.4 Indefinite Integrals--------------------------------------------------1

5.5 The Substitution Rule-------------------------------------------------2

TOTAL......................................................................53

Comment. The entire Calculus is based upon the notions of FUNCTIONS and

LIMITS; without a thorough understanding of those concepts, students will not

succeed in subsequent semesters. Pertinent sections of the syllabus (Review of

Chapter 1, Chapter 2, Section 4.4) should therefore receive particular

attention.