Course Title: Calculus-II
Type of Course: Compulsory, Theory, Non-departmental
Offered to: EEE
Pre-requisite Course(s): None
Complex Variable: Complex number system. General functions of a complex variable. Limits and continuity of functions of complex variables and related theorems. Complex differentiation and the Cauchy-Riemann equations. Infinite series. Convergence and uniform convergence. Line integral of complex functions. Cauchy's integral formula. Liouville's theorem. Taylor's and Laurent's theorem. Singular points. Residue, Cauchy's residue theorem.
Vector Analysis: Multiple product of vectors. Linear dependence and independence of vectors. Differentiation and integration of vectors together with elementary applications. Line, surface and volume integrals. Gradient of a scalar function. divergence and curl of a vector function. Various formulae. Integral forms of gradient, divergence and curl. Gauss's divergence theorem, Stokes’ theorem and Green's theorem.
Along with their physical significance.
To establish sufficient knowledge to deal with different complex and vector function for applying in engineering problems.
To provide fundamental concept of complex and vector analyses
Fundamental concepts of differential calculus , integral calculus and geometry.
| CO No. | CO Statement | Corresponding PO(s)* | Domains and Taxonomy level(s) | Delivery Method(s) and Activity(-ies) | Assessment Tool(s) |
|---|---|---|---|---|---|
| 1 | Describe complex number system function of complex variable, vector algebra and vector valued function. | PO(a) | C2 | Lectures, Homework | Written exams; assignment |
| 2 | Explain different operations with complex variables, differentiation and integration of complex and vector function. | PO(a) | C2 | Lectures, Homework | Written exams; assignment |
| 3 | Use the concepts of differentiation and integration of complex and vector function for solving different type of problems |
PO(b) | C3 | Lectures, Homework | Written exams; assignment |
Cognitive Domain Taxonomy Levels: C1 – Knowledge, C2 – Comprehension, C3 – Application, C4 – Analysis, C5 – Synthesis, C6 – Evaluation, Affective Domain Taxonomy Levels: A1: Receive; A2: Respond; A3: Value (demonstrate); A4: Organize; A5: Characterize; Psychomotor Domain Taxonomy Levels: P1: Perception; P2: Set; P3: Guided Response; P4: Mechanism; P5: Complex Overt Response; P6: Adaptation; P7: Organization
Program Outcomes (PO): PO(a) Engineering Knowledge, PO(b) Problem Analysis, PO(c) Design/development Solution, PO(d) Investigation,
PO(e) Modern tool usage, PO(f) The Engineer and Society, PO(g) Environment and sustainability, PO(h) Ethics, PO(i) Individual work and team work,
PO(j). Communication, PO(k) Project management and finance, PO(l) Life-long Learning
* For details of program outcome (PO) statements, please see the departmental website or course curriculum
| K1 | K2 | K3 | K4 | K5 | K6 | K7 | K8 | P1 | P2 | P3 | P4 | P5 | P6 | P7 | A1 | A2 | A3 | A4 | A5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Week | Topics | Teacher's Initial/Remarks |
|---|---|---|
| Week-1 | Complex number system. | CO1 |
| Week-2 | General functions of a complex variable. | CO1 |
| Week-3 | Limit and continuity of functions of a complex variable and related theorems. | CO1 |
| Week-4 | Complex differentiation and the Cauchy-Riemann equations. | CO2 |
| Week-5 | Infinite series, convergence, and uniform convergence. | CO2 |
| Week-6 | Line integral of a complex function. | CO2 |
| Week-7 | Cauchy's integral formula | CO2 |
| Week-8 | Class Test | |
| Week-9 | Liouville's theorem, Taylor's theorem. | CO2 |
| Week-10 | Laurent's theorem. | CO2 |
| Week-11 | Singular points. | CO2 |
| Week-12 | Residue. | CO2 |
| Week-13 | Cauchy's residue theorem. | CO2 |
| Week-14 | Class Test |
Weekly schedule: For Vector Analysis
| Week | Topics | Teacher's Initial/Remarks |
|---|---|---|
| Week-1 | Multiple product of vectors. | CO3 |
| Week-2 | Linear dependence and Independence of vectors. | CO3 |
| Week-3 | Differentiation and integration of vectors. | CO3 |
| Week-4 | Solving problems related to differentiation and integration of vector functions. | CO3 |
| Week-5 | Gradient of scalar functions, divergence and curl of vector functions. | CO3 |
| Week-6 | Integral forms of gradient, divergence and curl. | CO3 |
| Week-7 | Class Test | |
| Week-8 | Line integrals. | CO4 |
| Week-9 | Green’s theorem and solving problems related to this theorem. | CO4 |
| Week-10 | Surface and volume integrals. | CO4 |
| Week-11 | Gauss’s theorem and solving problems related to this theorem. | CO4 |
| Week-12 | Stokes theorem and solving problems related to this theorem | CO4 |
| Week-13 | Class Test | |
| Week-14 | Review Class |
Class Participation: Class participation and attendance will be recorded in every class.
Continuous Assessment: Continuous assessment any of the activities such as quizzes, assignment, presentation, etc. The scheme of the continuous assessment for the course will be declared on the first day of classes.
Final Examination: A comprehensive term final examination will be held at the end of the Term following the guideline of academic Council.
Class Participation 10%
Continuous Assessment 20%
Final Examination 70%
Total 100%
Complex Variables and Application by Ruel V. Churchill/James Ward Brown.
Schaum’s Outline of Theory and Problems of Complex Variables by Murray R. Spiegel.
Calculus by Howard Anton, Irl Bivens and Stephen Davis.
Schaum’s Outline of Theory and Problems of Vector Analysis by Murray R. Spiegel.
Advanced Engineering Mathematics by Peter V. O’ Neil.
Complex Variables: Harmonic and Analytic Functions by Francis J. Flangian.
Function Of Complex Variable by M.L. Khanna.
Vector Analysis by M.D. Raisinghania.
Advanced Engineering Mathematics by Erwin Kreyszig, Herbert Kreyszig and Edward J. Norminton.
Vector Analysis with Applications by Md. Ali Ashraf and Md. Abdul Khaleq Hazra.