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- 11 Jul 2022
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Upon completion of this subject, the students should be able to:
- Solve systems of linear equations using a variety of techniques.
- Utilise properties and techniques of matrix algebra to solve and analyse systems of equations.
- Solve ordinary differential equations of first and second order.
- Apply appropriate techniques to construct and solve definite and indefinite integrals.
- Determine the convergent / divergent nature of sequences and series and compute their limiting behaviour.
- Analyse and plot parametric and polar equations, and compute properties associated with them.
- Linear Equations and Matrices Section
- Linear equations in matrix form and Gauss-Jordan reduction.
- Matrix arithmetic, inverse matrices, determinant, and invertibility.
- Row operations as matrix multiplications, elementary matrices.
- Linear transformations. Eigenproblems: eigenvalues, eigenvectors, characteristic equation.
- Ordinary Differential Equations (ODEs)
- First order ODEs: separable equation, integrating factor technique,
- Euler's Method. Systems of first order, linear ODEs solved as an eigenvalue problem. 2nd order ODEs – oscillating systems (spring).
- Techniques of Integration
- Integration by Parts, Reduction formulae. Trigonometric substitutions. Rational Functions & Partial Fractions.
- Applications of Integration
- Riemann sum approach. Mass from Lineal Density. Work, Hydrostatic Pressure, and Force. Arc Length. Blood Flow, Flux.
- Numerical Integration
- Mid-Point, Trapezoidal, and Simpson's Rules. Error Bounds.
- Improper Integrals
- Convergence, Divergence
- Infinite Sequences and Series
- Sequences: convergence, divergence. Series - partial sums.
- Test for divergence, Integral test - comparison test for convergence.
- Ratio Test. Alternating series. Absolute and conditional convergence.
- Power Series
- Convergence Tests. Taylor Series, Maclaurin Series, and Binomial Series. Applications of Taylor Series.
- Parametric Equations & Polar Coordinates
- Introduction. Tangents, Areas, Curve Sketching, and Arc Lengths using the Riemann Approach
No eligibility requirements
No additional requirements
This subject is a continuation of KMA152, with emphasis on the application of single-variable calculus and linear algebra to problems in mathematics, the physical and biological sciences, economics, and engineering. The subjects KMA152 and KMA154 also provide an excellent introduction to the mathematical rigour required for higher level mathematics based subjects.
- Weekly online quizzes (20%)
- Final Exam (40%)
- Written Assignments (40%)
Current study term: 10 Jul 22 to 16 Oct 22
Check the learning management system (LMS) of your university for textbook details.