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Main
UQU Programs
Mathematics

Numerical Analysis 1

MTH2501
3 hours English

Numerical Analysis 1

Numerical Analysis1
MTH1101 Calculus 1
3 hours No requisites
MTH1401 Linear Algebra 1
3 hours One requisite
1 Introduction: / Review of Calculus, Computer arithmetic, Errors; round-off error, Floating point arithmetic, truncation error
2 Numerical Solution of Nonlinear Equations: / Bisection method, Fixed point iteration, Newton-Raphson iteration, Secant method, Error analysis for iterative methods, Aitken- method
3 Interpolation and Polynomial Approximation: / Lagrange interpolation and the approximation error, Divided differences and Newton interpolation, Cubic spline interpolation
4 Numerical Differentiation and Integration: / Numerical Differentiation: Two and three points formulas for first and second derivatives, errors analysis. / Numerical Integration: Trapezoidal rule, Simpson’s rule
5 Revision
1.1 Mapped to: K2

Recognize the limitations of computer arithmetic and numerical methods.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm exam and final Exam.
1.2 Mapped to: K1

Explain the concept of errors, rate of convergence, direct methods, indirect methods, approximated solutions, and exact solutions

Teaching Strategy Lectures, problem-based learning
Assessment Methods Homework, Midterm exam and final Exam.
2.1 Mapped to: S2, S6

Find a zero of a function in one variable using the bisection, fixed point, Newton, and secant methods, and estimate the errors.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm exam and final Exam.
2.2 Mapped to: S2, S6, S7

Construct the interpolating polynomial of a set of points and estimate its error bound

Teaching Strategy Lectures, project report
Assessment Methods Homework, Midterm exam and final Exam.
2.3 Mapped to: S1, S2

Compute derivatives and integrals numerically.

Teaching Strategy Lectures, exercises
Assessment Methods Homework, Midterm exam and final Exam.
3.1 Mapped to: V1, V2

Develop self-learning skills and solve problems both individually and in collaboration with the classmates

Teaching Strategy Lectures, project report
Assessment Methods Homework and assignments.
Assessment
Weight
Midterm exam
30%
Homework and assignments
20%
Final Exam
50%
Total
100%