Topic Covered in the Textbook

Chapter 1
1.2 Round-off errors and computer arithmetic

YES: Concept of machine epsilon; limitation of finite precision calculations; ways
to avoid the problem of loss of significant digits.
NO: Number of bits/bytes used in the IEEE single/double precision. 

Chapter 2
2.1 Bisection method
2.2 Fixed-point iteration
2.3 Newton's method and its extensions
2.4 Error analysis for iterative methods

YES: Mean Value Theorem; Taylor series expansion; Intermediate Value Theorem; how to use Bisection method, fixed point iteration and Newton’s method; application of the fixed-point theorem (Theorem 2.3); order of convergence of a sequence. 
NO: Bisection/Newton’s method for more than 3 iterations. 

Chapter 3
3.1 Interpolation and the Lagrange polynomial
3.3 Divided differences

YES: Interpolation using the Lagrange interpolating polynomials and the Newton’s divided difference; error bound for using the polynomial interpolation; piecewise interpolation. 
NO: Interpolation with more than 3 data points. 

Chapter 4
4.1 Numerical Differentiation
4.3 Elements of numerical integration
4.4 Composite numerical integration
4.7 Gaussian quadrature

YES: Numerical differentiation; derivation of approximation rules using polynomial interpolation and Taylor expansion. Trapezoidal rule, Simpson's rule and Midpoint rule; Derivation of their error term; Degree of accuracy; Composite Trapezoidal/Simpson's/Midpoint rules. 
NO: Invert a linear system of size larger than 3-by-3. 

Chapter 6
6.1 Linear systems of equations
6.2 Pivoting strategies
6.3 Linear algebra and matrix inversion
6.5 Matrix factorization
6.6 Special types of matrices

YES: Gaussian elimination (GE) with backward substitution; with partial pivoting; LU decomposition; PA=LU decomposition.
NO: Number of operations for GE; Invert a linear system of size larger than 3-by-3. 

Chapter 7
7.1 Norms of vectors and matrices
7.3 The Jacobi and Gauss-Siedel iterative techniques
7.4 Relaxation techniques for solving linear systems
7.5 Error bounds and iterative refinement

YES: Vector and matrix norms; Jacobi, Gauss-Seidel and SOR iteration; Their matrix representations; Convergence of the classical iterative methods.  
NO: Invert a linear system of size larger than 3-by-3. 

Chapter 8
8.1 Discrete least squares approximation

YES: Normal equation; least squares approach with general set of basis.
NO: Invert a linear system of size larger than 3-by-3.

Chapter 5
5.1 The elementary theory of initial-value problems
5.2 Euler's method
5.3 High order Taylor methods
5.4 Runge-Kutta methods
5.9 Higher-order equations and systems of differential equations
5.11 Stiff ODE's

YES: Forward Euler method, backward Euler method, Trapezoidal method; their derivation, derivation of the local truncation error and the global error; Lipschitz constant; converting a high order ODE to a system of first order ODE; high order Taylor method; Runge Kutta; Interval of absolute stability
NO: The exact expressions for the local truncation error and the global error; table form of RK; RK4