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Engineering Mathematics II

Water Engineering · Level 6  ·  9 Chapters

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Chapters

1
Apply Calculus
33 topics
No Notes Yet
2
Apply Power Series
4 topics
No Notes Yet
3
Apply matrices II
9 topics
No Notes Yet
4
Apply multiple Integrals
4 topics
No Notes Yet
5
Solve Ordinary differential Equations
11 topics
No Notes Yet
6
Solve Partial differential equations
4 topics
No Notes Yet
7
Apply Fourier Series
3 topics
No Notes Yet
8
Apply Laplace transforms
15 topics
No Notes Yet
9
Apply Numerical methods
9 topics
No Notes Yet
What Engineering Mathematics II covers: 45 main topics in 9 chapters

1. Apply Calculus

  1. 1.1 Derivates of functions
  2. 1.2 Differentiation from first principles
  3. 1.3 Differentiation of parametric equations
  4. 1.4 Differentiation of implicit functions
  5. 1.5 Logarithmic differentiation
  6. 1.6 Integration using algebraic substitutions
  7. 1.7 Applications of integration
  8. 1.8 Further worked problems on integration using algebraic substitutions
  9. 1.9 Integration using trigonometric substitutions
  10. 1.10 Integration using partial fractions
  11. 1.11 Integration by parts

2. Apply Power Series

  1. 2.1 Meaning of the term power series
  2. 2.2 Taylor’s theorem
  3. 2.3 Deduction of Maclaurin’s theorem to obtain power series
  4. 2.4 Application of Taylor’s theorem and Maclaurin’s theorems in numerical work

3. Apply matrices II

  1. 3.1 Determinant of a 3 𝑥 3 matrix
  2. 3.2 Inverse of 3 𝑥 3 matrix
  3. 3.3 Solutions of linear simultaneous equations in 3 unknowns (Crammer’s rule, inverse method, use of dominants and Gaussian elimination)
  4. 3.4 Applications of matrices
  5. 3.5 Definition of Eigen values and Eigen Vectors (Eigen values, Eigenvectors, characteristics polynomials, distinct Eigen values, Normalized Eigen Vectors)
  6. 3.6 Calculation of Eigen values and Eigen Vectors
  7. 3.7 Explanation of function of matrices (similarity transformation and properties, exponential and meaning, logarithms of matrices)
  8. 3.8 Definition of Jordan form of a matrix
  9. 3.9 State transition matrix (properties of continuous time transition matrix for a linear time varying system)

4. Apply multiple Integrals

  1. 4.1 Definition of double and triple integrals
  2. 4.2 Apply double and triple integrals in polar, cylindrical and spherical coordinates.
  3. 4.3 Use of triple integrals in solving problems.

5. Solve Ordinary differential Equations

  1. 5.1 Formation and solution of 1st and 2nd order differential equations
  2. 5.2 Order by the determination of coefficients.
  3. 5.3 D-operator method
  4. 5.4 Applications of differential equations

6. Solve Partial differential equations

  1. 6.1 Definition of partial derivatives
  2. 6.2 Derivation of a function of two or more variables
  3. 6.3 Application of partial derivatives
  4. 6.4 Stationary points of functions of two variables.

7. Apply Fourier Series

  1. 7.1 Definition of Fourier series for a function
  2. 7.2 Determination of Fourier series for period 2π to T
  3. 7.3 Determination of the Fourier series for odd and even functions and half-range series

8. Apply Laplace transforms

  1. 8.1 Definition of Laplace transform of a functions
  2. 8.2 Determination of inverse Laplace transforms of partial fractions and a list of standards
  3. 8.3 Differential equations and simultaneous equations with constant coefficients and given initial conditions

9. Apply Numerical methods

  1. 9.1 Define numerical methods
  2. 9.2 Definition of interpolation and extrapolation
  3. 9.3 Application of interpolation and extrapolation
  4. 9.4 Harmonic analysis using numerical methods

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