Math 1c
TA:
Homework 7: Greens Theorem
Week 8
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate to
contact your TA (or rea
Math 1c
TA:
Homework 3: Applications of the Derivative in Rn
Week 3
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate to
c
Math 1c
TA:
Homework 4: More Applications of the Derivative in Rn
Week 4
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate
Math 1c
TA: Padraic Bartlett
Homework 8: Stokes Theorem
Week 9: Due 6/3/13
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesita
Math 1c
TA:
Homework 2: The Derivative in Rn
Week 2
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate to
contact your TA (
Homework Set 4, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or solutions) but you must give a precise reference. Each student must write up her or his solution
individually, even if th
Homework Set 5, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or solutions) but you must give a precise reference. Each student must write up her or his solution
individually, even if th
Homework Set 6, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or solutions) but you must give a precise reference. Each student must write up her or his solution
individually, even if th
Homework Set 3, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or solutions) but you must give a precise reference. Each student must write up her or his solution
individually, even if th
Homework Set 1, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or their
solutions) but you must give a precise reference. Each student must write up her or his
solution individually, even
Math 1c
TA:
Homework 7: Surfaces and the Integral in Rn
Week 7
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate to
contac
Math 1c
TA:
Homework 6: The Integral in Rn
Week 6
Caltech 2013
For details on the collaboration policy, due dates, etc., please refer to the Ma1c course
webpage. If you have any questions when working on the HW, please dont hesitate to
contact your TA (or
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 10: Jun 3, 5, 7
26
Conservative vector elds
In general, the line integral of a vector eld depends on the path. Howe
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 1: Apr 1, 3, 5
1
Course introduction, functions of several variables
Recall functions of one variable: f : R R. Gra
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 2: Apr 8, 10, 12
4
More on derivatives
f
x ,
Example 4.1. f (x, y ) = x2 y + y 3 . To compute
3
regarding y as a co
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 3: Apr 15, 17, 19
7
Extrema of functions of several variables
Recall the one-variable case: extrema attained at cri
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 4: Apr 22, 24, 26
10
More on constrained min/max, Linear Programming
Another point of view: let h(x, y, ) = f (x, y
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 5: Apr 29, May 1, 3
13
Multivariable Integration
b
Recall one-variable case: a f (x) dx is the area below the graph
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
16
More on change of variables
Example 16.1. R sin(x2 +y 2 )dxdy , where R is the region in the rst quadrant
bounded by
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 9: May 27 (Memorial Day), 29, 31
24
Stokes Theorem
Theorem 24.1 (Stokes Theorem). F is a dierentiable plane vector
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 7: May 13, 15, 17
19
More on parametrization of surfaces, area
The tangent plane locally approximates S , is spanne
Vector Calculus
Ma 1c, Spring 2013
Yi NI
Caltech
Class meeting time: MWF 10am11am
Classroom: 119 Kerckho
Oce hours: T 2-3pm, 251 Sloan
Week 8: May 20, 22, 24
22
Greens Theorem
Theorem 22.1 (Greens Theorem). F = (P, Q) is a continuously dierentiable
plane
Homework Set 2, Math1c, Spring 2017
Practical Track
You may use any result from your class notes or the textbook (except exercises or solutions) but you must give a precise reference. Each student must write up her or his solution
individually, even if th