MA 137A - Calculus for Engineers II

• Use Newton’s method to approximate the zeros of a function
• Find the differential of a function and use it to approximate error
• Integrate algebraic, exponential, trigonometric, logarithmic and inverse trigonometric functions
• Evaluate a definite integral by the limit of Riemann sums and by Fundamental Theorem of Calculus
• Use method of substitution to find indefinite and definite integrals
• Use method of integration by parts
• Integrate products and powers of trigonometric functions
• Integrate functions using partial fractions
• Integrate functions by using trigonometric substitution
• Find areas between curves
• Find volumes of solids of revolution using disk and washer methods

• Graphing of functions
• Derivatives of algebraic, exponential, trigonometric, inverse trig and logarithmic functions
• Limits of algebraic and trigonometric functions
• Implicit derivatives
• Graphing using relative extrema

• Newton’s method of approximating zeros of a function (1 class)
• Differentials (1 class)
• Area problem and indefinite integrals (6 classes)
• The definite integral as the limit of Riemann sums and the Fundamental Theorem of Calculus (3 classes)
• Integration by substitution ( 5 classes)
• Areas between curves (2 classes)
• Rectilinear motion (1 class)
• Volumes by disk and washers (2 classes)
• Integration by parts (3 classes)
• Integration of products and powers of trig functions (2 classes)
• Integration using partial fractions (3 classes)
• Integration using trigonometric substitutions ( 1 class)
• Integration using tables (2 classes)
• Numerical integration (2 classes)
• Review and tests (6 classes)