College in High School Course Syllabus
Math 0230
Analytic Geometry and Calculus 2
(4 CREDITS)
The textbook for this course is Calculus by Elgin H. Johnston and Jerold C. Mathews, first edition (Addison Wesley, 2002).
The following topics are covered in this course:
Techniques of Integration
- Review of substitution
- Trigonometric substitution
- Areas between curves
- Intregration by parts
- Partial fraction decomposition
- Numerical integration: Trapezoid Rule, Midpoint Rule, Simpon's Rule, including error bounds
Differential equations
- Modeling: Population models (Malthusian, logistic)
- Radioactive decay
- Models for motion (free fall with air resistance, bungee jumping)
- Euler's Method
- Separation of variables
- Second order equations: Constant coefficient homogeneous equations
- Inhomogeneous equations: Undetermined coefficients
- Forced oscillations, resonance
Applications of integration
- Volumes by cross section
- Volumes by shells
- Polar coordinates
- Arc length
- Areas of regions described in polar equations
- Improper integrals
Sequence and Series
- Taylor polynomials
- Taylor's Theorem with remainder: error estimates
- Convergence of sequences
- Numerical infinite series
- Convergence tests: comparison, root, ratio, integral, p-series
- Power series and Taylor series
- Binomial series
- Algebraic operations on power series
- Integration and differentiation of power series
Vectors
- Equations of a line: parametric and symmetric forms
- The dot product
- The cross product
- Equations of a plane
- Functions of several variables: graphs; level curves and surfaces
- Cylindrical and spherical coordinates