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.