Applied Mathematics I

Course Purpose
The goal is for students to be able to perform calculations for engineering problems in mechanical fields.
Learning Goals
Students learn differential equations, Laplace transforms, and vector analysis, and develop mathematical analysis skills for understanding, designing, and developing phenomena in linear mechanical systems.
Topic
Session 1Differential equations [1] First-order differential equations (1) Fundamentals of differential equations, variable separation form and homogeneous form
Session 2Differential equations [1] First-order differential equations (2) Linear differential equations and total differential equations
Session 3Differential equation [2] Second-order differential equation (1) Homogeneous second-order differential equation and non-homogeneous second-order differential equation
Session 4Differential equation [2] Second-order differential equation (1) Homogeneous second-order differential equation and non-homogeneous second-order differential equation
Session 5Differential equations [2] Second-order differential equations (2) Second-order linear differential equations and simultaneous differential equations
Session 6In-class (midterm) exam (differential equations)
Session 7Laplace transform (1) Laplace transform and inverse Laplace transform
Session 8Laplace transform (2) differential equation solution
Session 9Vector analysis (1) Inner and outer products of vectors
Session 10Vector analysis (2) Gradient, divergence, and rotation
Session 11Vector Analysis (3) Curves and line integrals
Session 12Vector Analysis (4) Surfaces and area segments
Session 13Vector Analysis (5) Gaussian divergence theorem
Session 14Vector Analysis (6) Stokes' theorem
Session 15In-class (final) exam (Laplace transform and vector analysis)
＊＊This content is based on April 1, 2025. For the latest syllabus information and details, please check the syllabus information inquiry page provided by the university.＊＊