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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.

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

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