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