ENG1005 Engineering mathematics

When you finish this unit, you should be able to:

1. 1

   Evaluate cross products of vectors, and use vectors to represent lines and planes.

2. 2

   Perform matrix algebra.

3. 3

   Solve up to 3x3 systems of linear equations and find eigenvalues and eigenvectors.

4. 4

   Use hyperbolic functions.

5. 5

   Evaluate improper integrals of elementary functions and use integration by parts.

6. 6

   Appreciate convergence of numeric and power series, construct Taylor series and estimate errors in numerical approximations .

7. 7

   Solve first order ordinary differential equations, including by separable variables and integrating factors.

8. 8

   Solve second order linear differential equations with constant coefficients.

9. 9

   Use differential equations to model simple engineering problems.

10. 10

    Evaluate and invert Laplace transforms and use them to solve ordinary differential equations.

11. 11

    Calculate partial derivatives, use the gradient vector to find directional derivatives, and find extreme values of two-variable functions.

12. 12

    Express and explain mathematical techniques and arguments clearly in words.