MH2811: Mathematics 2

Course Instructor

Course AIMS

This course prepares students for the solution and interpretation of practical problems encountered in engineering disciplines with emphasis given to strengthening your problem- solving abilities. This course is target at second year MSE students, and aims at equipping MSE students with the necessary mathematical knowledge in Materials Science and Engineering applications.

Intended Learning Outcomes

By the end of this course, you (as a student) would be able to:

1. Apply the methods taught to solve for the Fourier series of a given periodic function.
2. Calculate the Fourier integral of a given function
3. Describe the use of the partial derivative and relate it to slopes and gradients, and the use of the directional derivative
4. Apply the chain rule to solve for the partial derivative of functions with multiple levels of dependent parameters
5. Describe the formal definition of the double integral
6. Calculate volumes via the double integral
7. Demonstrate the ability to reverse the order of a given double integral
8. Solve first order ordinary differential equations of the separable, linear and exact types
9. Solve second order linear ordinary differential equations with constant coefficients
10. Perform the method of separation of variables to derive the solution to a given partial differential equation
11. Provide the solution for a given heat or wave equation
12. Derive the different parametric forms of a given line curve or a surface
13. Apply Green's Theorem to solve a given integral
14. Calculate the line integral of a given scalar function, and a given vector field
15. Solve for the surface integral of a given scalar function, and a given vector field
16. Provide interpretations of the line integral and the surface integral of a given function
17. Apply conservation of a vector field to solve for the line integral and explain the meaning in terms of work done
    

Course Content

• Fourier series
• Fourier integrals
• Partial differentiation
• The chain rule for partial derivatives
• Double integrals
• Reversing the order of integration
• Ordinary differential equations
• Partial differential equations, wave and heat equations
• Vector fields, curl, divergence
• Line integrals and surface integrals
• Parameterizing a surface or line curve
• Green's Theorem
• Conserved vector fields

Reading and References

• Advanced Engineering Mathematics, by Kreysgiz E, 9th or 10th edition, John Wiley & Sons.ISBN: 978-0470646137
• Calculus, by Thomas, Weir and Hass, published by Pearson. 13th edition. ISBN:9780321878960
• Correlation between first attempt marks and CA performance.