MA 124 Syllabus

Mathematics Department
Indiana University of Pennsylvania
Indiana, PA 15705

Course Number:		MA 124

Course Title:		Calculus II for Physics and Chemistry

Credits:		4 semester hours

Prerequisites:		MA123

Textbook:		Calculus&Mathematica  
			by Davis, Porta, and Uhl
			Addison Wesley

Revised:		8/93

Catalog Description:

Course Outline

2.	Accumulation
	2.04	Transforming Integrals
Substitution in integration, the normal distribution and random errors, work, area inside a polar plot
	2.05	2D Integrals and the Gauss-Green Formula
Double integrals as volumes under surfaces, Gauss-Green formula for finding double integrals, 3D bell-shaped surfaces
	2.06	More Tools and Measurements
Separating variables to solve differential equations, algebra of complex numbers, ea+ib = ea (cos b + i sin b), ln(-a)=ln(a) + i Pi for a<0, integration by parts, iteration formulas, sinh and cosh, gamma function, Sin Integral, Erf
	2.07	Traditional Pat Integration Procedures for Special Situations
Undetermined coefficients, partial fractions, integral of sin(ax)n cos(bx)m , trig substitution, hyperbolic trig substitution, integration by parts-more extensive coverage.

3.	2D and 3D Measurements
	3.01	Vectors
Addition and scalar multiplication, tangent vectors and tangent lines, dot product and length of vectors, projections, orthogonality, velocity and acceleration, 				parametric equations for lines in 3D.	
	3.02	Perpendicularity
Cross product, Planes in 3D, normal vectors to surfaces

	3.03	Gradient
Definition of gradient, level curves and surfaces, steepest descent, chain rule for functions of three variables, total differential, maxima and minima for multi-variable functions, Lagrange multipliers	
	3.04	Trajectories
Vector fields in 2D, trajectories in vector fields, Flow along a curve in 2D, Flow across a curve in 2D, Direction fields for a single first order DE, gradient fields.
	3.05	2D Measurements
Integrals along curves, flow along a curve in 2D, flow across a curve in 2D, independence of path, test for gradient fields, work
	3.06	Sources
Divergence, sources and sinks, rotation of a 2D vector field, the Laplacian operator
	3.07 	Transform 2D
Change of variable in 2D, the Jacobian and transforming 2D integrals, volume, mass, and density, linear transformations, eigenvalues and eigenvectors in 2D
	3.08	Transform 3D
3D integrals, transforming 3D integrals, average value of a function, switching the order of integration, centroids and center of mass, Jacobian
	3.09	Spherical
Spherical coordinates, integration in spherical coordinates, 4D spheres, eigenvalues and eigenvectors in 3D
	3.10	3D Measurement
Gauss' formula in 3D, surface area, surface integrals, measuring flow across surfaces, flux in electric fields
	3.11	3D Flowalong
Curl of a 3D vector field, Stokes' Theorem, path independence, work, irrotational fields and gradient fields

4.	Approximation
	4.01	Splines
Order of contact (f(a)=g(a), f'(a)=g'(a), f''(a)=g''(a), etc.), splines, 	piecewise-cubic splines
	4.02	Expansions in powers of x
Polynomial approximations, general formula, sin, cos, exponential, 1/1-x, substitution, differentiation, and integration to get other expansions
	4.03	Using Expansions
Newton's method for finding roots, using expansions to find limits, complex exponential function, using expansions to approximate integrals
	4.04	Taylor's Formula
Taylor's formula, numerical integration schemes based on Taylor expansions, numerical approximation to solutions of DEs (Euler and Runge-Kutta), L'Hopital's rule
	4.05	Barriers to Convergence
Intervals of convergence for Taylor series, intervals of convergence for f(x), f'(x), integral of f(x), infinite series of numbers, geometric series

	4.06	Power Series
Definition of power series, power series solutions of DE's, convergence test, ratio test