Calculus I

Course Purpose
The purpose of this course is for students to understand one-variable calculus, which is required to learn the sciences.
Learning Goals
Students will obtain the basic knowledge of one-variable calculus. Students will aim for being able to calculate, but also understand the meaning of the calculation.
Topic
Session 1Class guidance, limits of one-variable functions
Session 2Continuity of functions of one variable, intermediate value theorem
Session 3Fundamentals of differentiation of functions of one variable, derivatives, and formulas of differentiation
Session 4Exponential functions / Logarithmic functions / Trigonometric functions
Session 5Hyperbolic functions / Inverse trigonometric functions
Session 6Mean value theorem, l'Hopital theorem
Session 7Taylor's theorem, Taylor expansion, Euler's formula
Session 8Extreme values and curve outline, polar coordinates
Session 9Definition and properties of definite integral
Session 10Calculation of indefinite and definite integrals (replacement integral, partial integral)
Session 11Integration of rational functions, integration of irrational functions
Session 12Broad integral
Session 13Area / Volume / Length of curve
Session 14Summary and exercises
＊＊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.＊＊