course content
Advanced revised edition
Algebra: simplifying expressions and functions; Indicators; Linear and quadratic equations; Simultaneous linear equations; Unequal partial scores.
Trigonometry: the solution of triangle; Multi-angle formula; Trigonometric equation.
The following topics were studied and tested in two semesters:
1. Differentiation: basic rules; Differences between standard functions; Newton's method of finding roots; Local differentiation.
2. Integral: the definition of integral; Standard integral; Substitution; Part integration; Numerical integration.
3. Complex number: graphic representation; Algebraic polar coordinate form Euler formula and exponential form.
4. Differential equation: classification; Simple first and second order differential equations.
5. Function: reversing; Exponent, logarithm and hyperbola of trigonometric functions.
6. Distinguish: maximum value, minimum value and inflection point; Curve sketch; Parametric, implicit and logarithmic differential; Taylor and McLaughlin series.
7. Integration: substitution; Application of center of mass, rotation, etc.
8. Integration: reasonable function; The integral is incorrect.
9. Integral: double integral; Polar coordinates; Triple integral.
10. Differential equation: the solution of first-order ordinary differential equation (separable, homogeneous, linear and accurate).
1 1. Differential equation: linear operator; Linear nonhomogeneous second order ordinary differential equation; ; Free oscillator and forced oscillator.
12. Vector: basic attribute; Cartesian component, scalar and vector product.
13. Vector: triple product; Differential and integral of vectors; Vector equations of lines and planes.
14. Matrix algebra: terminology; Addition, subtraction and multiplication of matrices; Determinant.
15. Matrix algebra: matrix inversion using auxiliary factors; Linear equation; Find the inverse of matrix by elimination method.
16. Matrix algebra: hierarchical structure; Eigenvalues and eigenvectors.
17. Further calculus: chain rule of partial derivatives; Total difference and small error of higher order partial derivatives.
18. Complex number: trigonometric function, hyperbolic function; Logarithm of complex number; De Morville theorem; Simple locus on the complex plane of roots.
19. Statistics: probability; Conditional probability combination and permutation; Discrete and continuous random variables.
20. Statistics: mean and standard deviation of sample data; Normal distribution sampling; Confidence interval; Hypothesis test.