2301108 CALCULUS II
Course Number  2301108  

Course Credits  3 (306)  
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  /  CU1.1: Behavioral Objectives Possessing wellrounded knowledge 
/  CU1.2: Possessing indepth knowledge  
/  CU2.1: Being moral and ethical  
/  CU2.2: Having an awareness of etiquette  
/  CU3.1: Being able to think critically  
/  CU3.2: Being able to think creatively  
/  CU3.3: Having skills in problem solving  
/  CU4.1: Having professional skills  
CU4.2: Having communication skills  
CU4.3: Having skills in information technology  
/  CU4.4: Having mathematical and statistical skills  
/  CU4.5: Having management skills  
/  CU5.1: Having an inquiring mind  
/  CU5.2: Knowing how to learn  
CU5.3: Having leadership qualities  
CU5.4: Maintaining wellbeing  
CU5.5: Being communityminded and possessing social responsibility  
CU5.6: 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 biotechnologyrelated 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 realvalued function of 2 and 3 variables.  
21. Students can determine the partial derivatives of the realvalued 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 `%  
Midterm examination  45 %  
Final examination  40 %  
Class attendance  5 %  
Grading  Grading System  Letter Grad (AF)  
Grading method  Normreferenced 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., PrenticeHall, 2002.  None  
Textbook  Thomas and Finney, Calculus and Analytic Geometry, 9th ed., AddisonWesley, 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 