Course Name: Advanced Mathematics D

Course Code: ZJ001SX24D

Course Credit: 4

Course Type: Professional Foundation Course

Applicable Major: Industrial Design and Product Design

Course Introduction

Advanced Mathematics D is a basic course for students majoring in design, architecture, city planning, etc. The main content is the basic knowledge of calculus of one and two variables, ordinary differential equations and linear algebra. The specific contents are as follows: the concept and properties of functions, elementary functions, limits of a sequence, infinite series, limits of a function, the concept and properties of continuous functions, the derivative and the differential of a function, the mean value theorem of the differential calculus, L'Hospital's rule, the monotonicity and extreme values of a function, the maximum and minimum of a function, the concavity or convexity and inflection points of a curve, the concept and  evaluation of indefinite integrals, the concept and properties of definite integrals, the fundamental theorem of calculus, the Newton-Leibniz formula, methods of evaluating definite integrals, improper integrals, limits and continuity of a function of two variables, partial derivatives and total differential of a function of two variables, derivatives of the composite of functions of two variables, derivatives of implicit functions, properties and calculations of double integrals, first-order ordinary differential equations, the concept and properties of determinants, evaluating a determinant by expanding along a row or a column, the concept and operations of matrices, invertible matrices, elementary transformations of matrices, solving a system of linear equations by elementary transformations, the rank of a matrix, conditions for the solvability of a system of linear equations, eigenvalues and eigenvectors of matrices, positive definite matrices. The goal of the course is to equip students with the fundamentals of calculus and linear algebra and to prepare them for the mathematical foundation they need for subsequent courses.