On successful completion of this subject, students should be able to:

1. Recognise and solve various types of first and second order differential equations and some higher order ordinary differential equations
2. Set up a linear 2D system of differential equations and investigate its solution and the nature of its critical points
3. Apply Laplace transforms in solving problems
4. Use multivariable calculus techniques competently
5. Evaluate multiple (double and triple) integrals.

First Order Ordinary Differential Equations - Separable and linear equations and applications.
Second Order Linear ODEs- both homogeneous and non homogeneous with constant coefficients and applications, Euler Cauchy and Power series solutions.
Higher Order ODEs - homogeneous and non homogeneous with constant coefficients and Euler-Cauchy.
2D linear constant coefficient homogeneous systems, phase plane, critical points and criteria for critical points.
Laplace Transforms and solving ODEs using Laplace transforms.
Level curves and sketching regions in space
Limits and continuity of functions of two variables
Partial differentiation
Chain rule
Gradient vectors and directional derivatives
Equations of normal lines and tangent planes
Maxima, minima and saddle points
Lagrange multipliers
Double integrals in rectangular and polar coordinates and applications
Triple integrals in rectangular, cylindrical and spherical coordinates and applications.
1. First Order Ordinary Differential Equations - Separable and linear equations and applications.
2. Second Order Linear ODEs- both homogeneous and non homogeneous with constant coefficients and applications, Euler Cauchy and Power series solutions.
3. Higher Order ODEs - homogeneous and non homogeneous with constant coefficients and Euler-Cauchy.
4. 2D linear constant coefficient homogeneous systems, phase plane, critical points and criteria for critical points.
5. Laplace Transforms and solving ODEs using Laplace transforms.
6. Level curves and sketching regions in space
7. Limits and continuity of functions of two variables
8. Partial differentiation
9. Chain rule
10. Gradient vectors and directional derivatives
11. Equations of normal lines and tangent planes
12. Maxima, minima and saddle points
13. Lagrange multipliers
14. Double integrals in rectangular and polar coordinates and applications
15. Triple integrals in rectangular, cylindrical and spherical coordinates and applications
15. Triple integrals in rectangular, cylindrical and spherical coordinates and applications.