# Calculus 1

1. Course Prerequisites:This course is designed for students who have learned algebra, geometry, trigonometry, and precalculus.2. DayTime:WenSat 6:30-7:30pm (Tentative)

3. Major Topics to be covered:01 Functions,

02 New Functions from Old,

03 Families of Functions

04 Inverse Functions; Inverse Trigonometric Functions ,05 Exponential and Logarithmic Functions

06 Limits (An Intuitive Approach)07 Computing Limits

08 Limits at Inﬁnity; End Behavior of a Function

09 Limits (More Rigorously),10 Continuity,

11 Continuity of Trigonometric, Exponential, and Inverse Functions

12 Tangent Lines Rates of Change,13 The Derivative Function,

14 Introduction to Techniques of Differentiation

15 The Product and Quotient Rules,16 Derivatives of Trigonometric Functions,

17 The Chain Rule

18 Implicit Differentiation ,19 Derivatives of Logarithmic Functions

20 Derivatives of Exponential and Inverse Trigonometric Functions,21 Related Rates

22 Local Linear Approximation; Differentials,23 L’Hôpital’s Rule; Indeterminate Forms

24 Analysis I: Increase, Decrease, and Concavity,25 Analysis II: Relative Extrema; Graphing Polynomials

26 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents,27 Absolute Maxima and Minima

28 Applied Maximum and Minimum Problems,29 Rectilinear Motion,

30 Newton’s Method

31 Rolle’s Theorem; Mean-Value Theorem,32 An Overview of the Area Problem , 5.2 The Indeﬁnite Integral

33 Integration by Substitution ,34 The Deﬁnition of Area as a Limit; Sigma Notation,

35 The Deﬁnite Integral

36 Fundamental Theorem,37 Rectilinear Motion,

36 Average Value of a Function and its Applications

39 Evaluating Deﬁnite Integrals by Substitution,40 Logarithmic and Other Functions Deﬁned by Integrals