Math 83


TECHNICAL CALCULUS (4:4:0) Limits, derivatives of algebraic functions,
implicit differentiation, related rates, applied extrema problems,
curve sketching, integration, numerical integration, applications of
integration, integration techniques, differential equations.

 Prerequisite: Math 82.


Text: Basic Technical Mathematics w/Calculus. Fifth Edition. 
Allyn J. Washington, Addison-Wesley, 1990.

  Chapter   Sections   Topics                                                            
    22          1      Limits                                                                
                2      The Slope of a Tangent to a Curve                                     
                3      The Derivative                                                        
                4      The Meaning of the Derivative                                         
                5      Derivatives of Polynomials                                            
                6      Derivatives of Products and Quotients                                 
                7      The Derivative of a Power of a Function                               
                8      Differentiation of Implicit Functions                                 
                9      Higher Derivatives

                                                    
    23          1      Tangents and Normals                                                  
                2      Newton's Method for Solving Equations                                 
                3      Curvilinear Motion                                                    
                       REVIEW                                                                
                       EXAMINATION I                                                         
                4      Related Rates I                                                       
                4      Related Rates II                                                      
                5      Using Derivatives in Curve Sketching                                  
                6      More on Curve Sketching                                               
                7      Applied Maximum and Minimum Problems I                                
                7      Applied Maximum and Minimum Problems II

                               
    24          1      Differentials                                                         
                2      Antiderivatives                                                       
                3      The Indefinite Integral                                               
                4      The Area Under a Curve                                                
                5      The Definite Integral I                                               
                5      The Definite Integral II                                              
                6      Numerical Integration; The Trapezoidal Rule                           
                7      Simpson's Rule                                                        
                8      REVIEW                                                                
                       EXAMINATION II

                                                          
    25          1      Applications of the Indefinite Integral                               
                2      Areas by Integration I                                                
                2      Areas by Integration II                                               
                3      Volumes by Integration I                                              
                3      Volumes by Integration II                                             
                4      Centroids                                                             
                5      Moments of Inertia                                                    
                6      Other Applications                                                    
                8      REVIEW 

                                                               
    26          1      Derivatives of Sine and Cosine                                        
                2      Derivatives of Other Trigonometric Functions                          
                3      Derivatives of Inverse Trigonometric Functions                        
                4      Applications                                                          
                5      Derivative of the Logarithmic Function                                
                6      Derivative of the Exponential Function                                
                7      Applications                                                          
                8      REVIEW                                                                
                       EXAMINATION III                                                         

    27          1      The General Power Formula                                             
                2      The Basic Logarithmic Form                                            
                3      The Exponential Form                                                  
                4      The Basic Trigonometric Forms                                         
                7      Integration by Parts                                                  
                9      Integration by Use of Tables                                          
                       Integration with the aid of Algebraic Manipulators, 
                       eg. Derive

        
    28          1      Solutions of Differential Equations                                   
                2      Separation of Variables                                               
                4      First Order Linear Differential Equations                             
                5      Elementary Applications                                               
                6      Second Order Homogeneous Equations with Constant
                       Coefficients
         
                       REVIEW

                                                                
                       FINAL EXAMINATION