Part I  Single Variable Calculus

    Chapter 1. Functions

 1.1 Functions and Graph     Solution

 1.2 Symmetry      Solution

1.3 Common Functions  Solution

1.4 Translation, Stretching and Rotation of Functions  Solution

     Chapter 2. Limits and Continuity

2.1 Limits of functions             

2.2 Continuity 

      Chapter 3. Derivatives

3.1 Definition of Derivatives, Differentiation 

3.2 Derivatives of Basic Functions, The Product and Quotient Rule 

3.3 The Chain Rule and Inverse Functions  

*3.4 Approximation and Related Rates    

      Chapter 4. Applications of Derivatives

4.1 Extreme values of a function      

4.2 The Shape of a Graph         

4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule     

4.4 Optimization Problems         

4.5 Newton’s Method      

   Chapter 5. Integrals

5.1 Areas and Distances          

5.2 The Definite Integral                   

5.3 The Fundamental Theorem of Calculus       

5.4 Indefinite Integrals and the Net Change Theorem     

5.5 The Substitution Rule      

5.6 The Logarithm Defined as an Integral         

   Chapter 6. Applications of Integration

6.1 Areas between Curves          

6.2 Volumes              

6.3 Volumes by Cylindrical Shells     

*6.4 Work           

6.5 Average Value of a Function        

     Chapter 7. Techniques of Integration

7.1 Integration by Parts          

7.2 Trigonometric Integrals        

7.3 Trigonometric Substitution        

7.4 Integration of Rational Functions and CAS              

7.5 Formulas for Integration       

*7.6 Integration Using Tables         

*7.7 Approximate Integration and CAS     

 7.8 Improper Integrals                               

      Chapter 8. Further Applications of Integration

8.1 Arc Length      

8.2 Area of a Surface of Revolution     

8.3 Center of Mass   

*8.4 Differential equations    

     Chapter  9. Infinite Sequences and Infinite Series

9.1 Sequences and Series              

9.2 Tests for convergence of series with positive terms           

9.3 Alternating Series and Absolute Convergence                  

9.4 Power Series                                      

9.5 Taylor, Maclaurin, and Binomial Series                  

     Chapter 10. Parametric Equations and Polar Coordinates

10.1 Parametric Equations                                            

10.2 Calculus with Parametric Curves                   

10.3 Polar Coordinates                             

10.4 Areas and Lengths in Polar Coordinates      

10.5 Conic Sections   


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