Examination

Report

1. Vector Algebra and Space Analytic Geometry
• The three dimensional rectangular coordinate system;
• Vectors and operations (including addition, subtraction and scalar multiplication; dot product, cross product and scalar triple product);
• Surfaces and equations;
• Space curves and equations;
• Planes and equations;
• Space lines and equations;
• Quadratic surfaces.

2. Multivariable Differential Calculus
• Basic concepts of multivariable functions;
• Partial derivatives;
• Total differential and applications;
• The chain rule;
• Implicit differentiation;
• Applications of the differential calculus for geometry;
• Directional derivatives and gradient;
• Extrema of multivariable functions;
• Taylor&#39;s theorem for functions of two variables.

3. Multivariable Integral Calculus
• Concepts, properties and calculation of double integrals (in both rectangular coordinate system and polar coordinate system);
• Applications of double integrals;
• Concepts, properties and calculation of triple integrals;
• Triple integrals in cylindrical coordinates and spherical coordinates;
• Line integrals with respect to arc length and coordinates (concepts, calculation and relationship);
• Green&#39;s theorem and applications;
• Surface integrals with respect to area and coordinates (concept, calculation and relationship);
• The divergence theorem and Stokes&#39; theorem;
• Introduction to flux and divergence, circulation and rotation.

4. Infinite Series
• Concepts, properties, and convergence tests of infinite series;
• Power series;
• Taylor series and applications;
• Fourier series;
• Sine series and cosine series;
• The Fourier series expansion with period of 21;
• Fourier series in complex form.

Foundation Mathematics for Engineering and Technology 2 - 3103CIT

Foundation Mathematics for Engineering and Technology 2

Know how to find the equations of the plane and line.

Know how to expanding function into power series.

Perform techniques of differentiation in problems relevant to engineering and technology.

Perform Green theorem to evaluate line integrals.

Perform techniques of integration in problems relevant to engineering and technology.