2301108 CALCULUS II
| Course Number | 2301108 | |
|---|---|---|
| Course Credits | 3 (3-0-6) | |
| Course Abbrviation | CALCULUS II | |
| Course Title (TH) | แคลคูลัส 2 | |
| Course Title (EN) | Calculus II | |
| Responsible Unit | Faculty of Science, Department of Mathematics and Computer Science | |
| Type of Course | International Course | |
| Semester | Intl 2nd semester | |
| Academic Year | 2024 | |
| Course Coordinator | ||
| Measurement Method | ||
| Type of Course | Semester Course | |
| Course Condition | Prerequisite 2301107 | |
| Course Status | Required courses | |
| Instructors / staffs | ||
| Enrollment conditions | None | |
| Degree level | Bachelor | |
| Related curricular | Bachelor of Science in Biotechnology (2562) | |
| Bachelor of Science in Biotechnology (2567) | ||
| Course description (TH) | อุปนัยเชิงคณิตศาสตร์ ลําดับและอนุกรมของจํานวนจริง การกระจายแบบอนุกรมเทย์เลอร์และการประมาณค่า ฟังก์ชันมูลฐาน การอินทิเกรตเชิงตัวเลข เวกเตอร์ เส้นตรงและระนาบในปริภูมิสามมิติ แคลคูลัสของฟังก์ชันค่าเวกเตอร์ของหนึ่งตัวแปร แคลคูลัสของฟังก์ชันค่าจริงของสองตัวแปร บทนําสู่สมการเชิงอนุพันธ์และการประยุกต์ | |
| Course description (EN) | Mathematical induction; sequences and series of real numbers; Taylor series expansion and approximation of elementary functions; numerical integration; vectors, lines and planes in three dimensional space; calculus of vector valued functions of one variable; calculus of real valued functions of two variables; introduction to differential equations and their applications. |
|
| Curriculum mapping | / | CU-1.1: Behavioral Objectives Possessing well-rounded knowledge |
| / | CU-1.2: Possessing in-depth knowledge | |
| / | CU-2.1: Being moral and ethical | |
| / | CU-2.2: Having an awareness of etiquette | |
| / | CU-3.1: Being able to think critically | |
| / | CU-3.2: Being able to think creatively | |
| / | CU-3.3: Having skills in problem solving | |
| / | CU-4.1: Having professional skills | |
| CU-4.2: Having communication skills | ||
| CU-4.3: Having skills in information technology | ||
| / | CU-4.4: Having mathematical and statistical skills | |
| / | CU-4.5: Having management skills | |
| / | CU-5.1: Having an inquiring mind | |
| / | CU-5.2: Knowing how to learn | |
| CU-5.3: Having leadership qualities | ||
| CU-5.4: Maintaining well-being | ||
| CU-5.5: Being community-minded and possessing social responsibility | ||
| CU-5.6: Sustaining Thainess in a globalized world | ||
| / | subPLO1.1 Explain biotechnology knowledge in practice. | |
| subPLO1.2 Analyze biotechnology knowledge in practice. | ||
| subPLO1.3 Apply biotechnology knowledge in practice. | ||
| PLO2 Employ biotechnology-related technology and scientific tools. | ||
| PLO3 Communicate effectively in English within the Biotechnology field. | ||
| PLO4 Demonstrate behavior that aligns with ethical principles, moral values, and professional ethics. | ||
| PLO5 Demonstrate social responsibility, courage, and creativity. | ||
| Course learning outcome (CLO) | 1. Students can prove the mathematical formula using mathematical induction. | |
| 2. Students can determine the convergence of sequences of real numbers. | ||
| 3. Students can determine the convergence of series of real numbers. | ||
| 4. Students can find the Taylor series for a given function. | ||
| 5. Students can approximate the function via Taylor series expansion. | ||
| 6. Students can find the numerical approximations of the integral. | ||
| 7. Students can find the dot product and cross product of two vectors in three dimensional space. | ||
| 8. Students can use the cross product to identify the area of parallelogram and the volume of parallelepiped. | ||
| 9. Students can determine a line equation from the given criteria. | ||
| 10. Students can determine the distance from a point to a line and determine the angle between two lines. | ||
| 11. Students can determine whether two lines are skew. | ||
| 12. Students can determine a plane equation from the given criteria. | ||
| 13. Students can determine the distance from a point to a plane and determine the angle between two planes. | ||
| 14. Students can determine the angle between a line and a plane. | ||
| 15. Students can determine the limit and continuity of a vector function. | ||
| 16. Students can determine the derivative and integral of a vector function. | ||
| 17. Students can determine the tangent vector, normal vector and binormal vector of a vector function. | ||
| 18. Students can determine the curvature and skewness of a vector function at a given point. | ||
| 19. Students can determine the velocity, acceleration, tangential and normal components of acceleration of motion. | ||
| 20. Students can determine the limit and continuity of real-valued function of 2 and 3 variables. | ||
| 21. Students can determine the partial derivatives of the real-valued function of two variables. | ||
| 22. Students can use the chain rule to solve a related rate problem. | ||
| 23. Students can apply the total differential to a given problem. | ||
| 24. Students can approximate the function of 2 or 3 variables using the total differential. | ||
| 25. Students can find the double integral on the given domain. | ||
| 26. Students can change the order of integral in double integral from a given problem. | ||
| 27. Students can apply the double integral to compute the area, volume, mass, moment or moment of inertia. | ||
| 28. Students can solve the first order differential equation of the first degree. | ||
| 29. Students can derive the differential equation from a given problem. |
| # | Date | Time | Learning content | Instructor | CLO | Remark |
|---|---|---|---|---|---|---|
| 1 | Mathematical Inductio, Sequences | |||||
| Mathematical Inductio, Sequences | ||||||
| 2 | Series, Divergence Test, the Integral Test, The Comparison Test | |||||
| Series, Divergence Test, the Integral Test, The Comparison Test | ||||||
| 3 | Limit Comparison Test, Alternating Series | |||||
| Limit Comparison Test, Alternating Series | ||||||
| 4 | Absolute Convergence, Ratio Test and Root Test | |||||
| Absolute Convergence, Ratio Test and Root Test | ||||||
| 5 | Power Series, Representation of Functions as Power Series, Taylor and Maclaurin Series and Applications of Taylor Polynomial | |||||
| Power Series, Representation of Functions as Power Series, Taylor and Maclaurin Series and Applications of Taylor Polynomial | ||||||
| 6 | Three Dimensional Coordinate Systems, vectors, Dot Product and Cross Product, Equations of lines and planes | • | ||||
| Three Dimensional Coordinate Systems, vectors, Dot Product and Cross Product, Equations of lines and planes | ||||||
| 7 | Vector Functions, Space Curves, Derivatives and Integrals of Vector Functions | • | ||||
| Vector Functions, Space Curves, Derivatives and Integrals of Vector Functions | ||||||
| 8 | Arc Length and Curvature | • | ||||
| Arc Length and Curvature | ||||||
| 9 | Functions of Several Variables: Limit and Continuity, Partial derivatives | • | ||||
| Functions of Several Variables: Limit and Continuity, Partial derivatives | ||||||
| 10 | Tangent Planes and Linear Approximation | • | ||||
| Tangent Planes and Linear Approximation | ||||||
| 11 | The Chain rules, directional derivatives and the gradient vector, maximum and minimum values | • | ||||
| The Chain rules, directional derivatives and the gradient vector, maximum and minimum values | ||||||
| 12 | Double Intergrals over rectangles, Iterated Integrals, double integrals over general regions | • | ||||
| Double Intergrals over rectangles, Iterated Integrals, double integrals over general regions | ||||||
| 13 | Double integrals in polar coordinate | • | ||||
| Double integrals in polar coordinate | ||||||
| 14 | Differential Equations, Separable Equations, Homogeneous Differential Equations | • | ||||
| Differential Equations, Separable Equations, Homogeneous Differential Equations | ||||||
| 15 | Exact Differential Equations, Integrating Factor, Linear and Bernoulli differential equations | • | ||||
| Exact Differential Equations, Integrating Factor, Linear and Bernoulli differential equations |
| Teaching/learning media | Board, LCD projector, computer and visualizer, iPad | ||
| Communication channels / LMS | |||
| Type | Channel identifier / URL | Remarks | |
| Learning Management System (LMS) | |||
| Assessment method | Level of assessment | Related CLO | Percentage |
| Assignment | 10 `% | ||
| Mid-term examination | 45 % | ||
| Final examination | 40 % | ||
| Class attendance | 5 % | ||
| Grading | Grading System | Letter Grad (A-F) | |
| Grading method | Norm-referenced Grading (อิงกลุ่ม) | ||
| Minimum Passing Level (MPL) | |||
| Reading list | |||
| Type | Title | Remark | |
| Textbook | James Stewart, Calculus. 7th ed., Cengage Learning, 2012. | None | |
| Textbook | Kenneth H. Rosen, Discrete Mathematics and Its Applications, 5th ed., McGraw Hill, 2003. | None | |
| Textbook | Howard Anton, et al, Calculus with Analytic Geometry. 7th ed., Wiley, 2002. | None | |
| Textbook | Henry Edwards and David Penney, Calculus with Analytic Geometry, 6th ed., Prentice-Hall, 2002. | None | |
| Textbook | Thomas and Finney, Calculus and Analytic Geometry, 9th ed., Addison-Wesley, 1996. | None | |
| Course evaluation | Course evaluation system | myCourseVille | |
| Details of improvement from previous evaluation | More examples will be provided | ||
| Course quality control | Responses to complaints / petitions from students |