CALCULUS OF SEVERAL REAL VARIABLES TYPE OF COURSE : Rerun | Core | UG COURSE DURATION : 8 weeks (17 Aug’20 - 9 Oct’20) EXAM DATE : 18 Oct 2020 PRE-REQUISITES : Calculus of One Real Variable INTENDED AUDIENCE : UG PROF. JOYDEEP DUTTA Department of Mathematics IIT Kanpur COURSE OUTLINE : This course introduces Calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, multiple integrals and their applications and end with the Stoke s Theorem and Gauss divergence theorem. ABOUT INSTRUCTOR : Prof. Joydeep Dutta is a Professor in the Department of Economic Sciences at IIT Kanpur. His research interest lies in convex analysis and optimization. He has given several MOOC courses including “Calculus of one real variable”. Calculus continues to fascinate him and intrigue him. COURSE PLAN : Week 1: Vectors and Matrices Week 2: Functions of several variables and partial derivatives Week 3: IFT, Taylorʼs Theorem, Maxima and Minima Week 4: Lagrange Multiplier Rule Week 5: Multiple Integrals Week 6: Line Integrals Week 7: Surface Integrals Week 8: Greenʼs Theorem, Strokes Theorem and Gauss Divergence Theorem
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CALCULUS OF SEVERAL REAL VARIABLES
TYPE OF COURSE : Rerun | Core | UGCOURSE DURATION : 8 weeks (17 Aug’20 - 9 Oct’20) EXAM DATE : 18 Oct 2020
PRE-REQUISITES : Calculus of One Real Variable
INTENDED AUDIENCE : UG
PROF. JOYDEEP DUTTA Department of Mathematics IIT Kanpur
COURSE OUTLINE :
This course introduces Calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, multiple integrals and their applications and end with the Stoke s Theorem and Gauss divergence theorem.
ABOUT INSTRUCTOR :
Prof. Joydeep Dutta is a Professor in the Department of Economic Sciences at IIT Kanpur. His research interest lies in convex analysis and optimization. He has given several MOOC courses including “Calculus of one real variable”. Calculus continues to fascinate him and intrigue him.
COURSE PLAN :
Week 1: Vectors and Matrices
Week 2: Functions of several variables and partial derivatives
Week 3: IFT, Taylorʼs Theorem, Maxima and Minima
Week 4: Lagrange Multiplier Rule
Week 5: Multiple Integrals
Week 6: Line Integrals
Week 7: Surface Integrals
Week 8: Greenʼs Theorem, Strokes Theorem and Gauss Divergence Theorem
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