# Calculus II Honors

Here are links of PowerPoint Presentations, PDF documents and Word documents.

## Topics

Systems of Equations, Gauss Seidel, Jacobi Gaussian Elimination, Induction, Well Ordering Principle, Real Space, Complex Space, Linear Spaces, Norm, Projection, Linear Independence, Linear Dependence, Basis, Vector Parametric Equation, Plane Parametric Equation, Cartesian Equation, Normal Vector, Subspaces, Nullspace, Range, Column Space, Linear Transformations and Matrices, A = LU factorization, Transformations, Rotation, Projection, Reflection, Shear, Change of Basis, Recurrence, Least Squares, Gram Schmidt A=QR, Schur Decomposition, Householder Reflection Matrix, Single Value Decomposition, L'Hopitals Rule, Mean Value Theorem, Diagonalization, Properties of Determinants, Eigenvalues and Eigenvectors, Recursions, Systems of Differential Equations, one repeated root, two distinct roots, imaginary root, First Order, Separable, Euclidean Spaces, Cross Product, Symmetric, Hermitian, Skew, Matrix, Cayley Hamilton, Complex Inner Products, Series Solutions to Differential Equations, Differentiation by Superposition, by Diagonalization, Infinite Series, Telescoping, Geometric, Harmonic, Basic Convergence test, Partial Fractions, P Series, Alternating Series Test, Absolute Convergence Test, Integral Test, Comparison Test, Limit Comparison Test, Root Test, Ratio Test, intermediate Value Theorem, Taylor Polynomials, and Taylor Series.

MATH 1512 course taken at the Georgia Institute of Technology.

## Strategy

Lesson Learned: You should be demanding proofs to your professors.

Practice makes perfect. Between tutors, TA's and profesors, the professor is the best resource for explanations.

## Course Materials