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