<Mathematics with CAS> by SGLee

<Linear Algebra (선형대수학) with Sage>

<Calculus  (미적분학) with Sage>

<미적분학 with Sage>

http://matrix.skku.ac.kr/Sage-Calculus/Web-Cover/

(2013 Spring Calculus with Sage Lectures (Youtube 동영상 강의)

Calculus with Sage Week 1 how to manage our class Review : http://youtu.be/XWEQFlv4jKc

Chapter 1. Functions http://youtu.be/cl8GqIWIRD0 (동영상 강의)

1.1 Functions and its graph  (문제 풀이)
(문제 풀이)
(문제 풀이)
(문제 풀이)

1.5 A Few Basic Concepts

Chapter 2. Limits and Continuity

Chapter 3. Theory of Differentiation

Chapter 4. Applications of Differentiation

Chapter 5. Integrals

Midterm Exam : 4월 24일 수요일 4시에 강의실

미적분학 with Sage Midterm Exam, SKKU SGLee http://youtu.be/QAEI7A2DMMM

Chapter 6. Applications of Integration
미적분학 with Sage Sec-6-1 Areas between Curves, SKKU SGLee http://youtu.be/o53phm5cqJE
미적분학 with Sage Sec-6-2 Volumes, SKKU SGLee http://youtu.be/4-ChOAFbJAs
미적분학 with Sage Sec-6-3 Volumes by Cylindrical Shells, SKKU SGLee http://youtu.be/qM1izf8qeX8

미적분학 with Sage Sec-6-4 Work by SKKU SGLee : http://youtu.be/u3ZaJWhKy6k
미적분학 with Sage Sec-6-5 Average Value of a Function by SKKU SGLee http://youtu.be/zmEeGmwQTB0

Chapter 7. Techniques of Integration
미적분학 with Sage Sec-7-1 Integration by Parts by SKKU SGLee : http://youtu.be/WX-6C9tCneE
미적분학 with Sage Sec-7-2 Trigonometric Integrals by SKKU SGLee : http://youtu.be/sIR0zNGQbus
미적분학 with Sage Sec-7-3 Trigonometric Substitution by SKKU SGLee : http://youtu.be/avTqiEUi8u8
미적분학 with Sage Sec-7-4 Integration of Rational Functions by the Method of Partial Fractions  by SKKU SGLee : http://youtu.be/KLTHp_7G4cI
미적분학 with Sage Sec-7-5 Guidelines for Integration  by SKKU SGLee : http://youtu.be/Fgn8U4We60o
미적분학 with Sage Sec-7-6 Integration Using Tables   by SKKU SGLee : http://youtu.be/tn9jLkgTMp8
미적분학 with Sage Sec-7-7 Approximate Integration  by SKKU SGLee : http://youtu.be/hg2pw1n1cZI
미적분학 with Sage Sec-7-8 Improper Integrals  by SKKU SGLee : http://youtu.be/rquxbYrC0Yc

Chapter 8. Further Applications of Integration

미적분학 with Sage Sec-8-1 Arc Length by SKKU : http://youtu.be/7OVqI20z_Bw

미적분학 with Sage Sec-8-2 Area of a Surface of Revolution by SKKU : http://youtu.be/Eq4i2A8eKxA

미적분학 with Sage Sec-8-3 Applications of Integral Calculus by SKKU : http://youtu.be/1ZAJeP16pAQ

*미적분학 with Sage Sec-8-4 Differential equations by SKKU : http://youtu.be/uHfOjz8I4-s

Chapter 9. Infinite Sequences and Infinite Series

9.1 미적분학 with Sage Sec-9.1 Sequences and Series   http://youtu.be/rz8ZS4Y_cvc
9.2 미적분학 with Sage Sec-9.2 Tests for convergence of series with positive terms  http://youtu.be/mxwSv6ApZ2g
9.3 미적분학 with Sage 9.3 Alternating Series and Absolute Convergence  http://youtu.be/NtSitFNv9Mk

9.4 미적분학 with Sage Sec 9.4 Power Series  http://youtu.be/426kkrMArgs
9.5 미적분학 with Sage Sec 9.5 Taylor, Maclaurin, and Binomial Series http://youtu.be/3zSPSvYHJQI

Chapter 10. Parametric Equations and Polar Coordinates

10.1 Parametric Equations  http://youtu.be/hQGCZk1tpuA
10.2 Calculus with Parametric Curves http://youtu.be/QFMSbGKhoX4
10.3 Polar Coordinates    http://youtu.be/lKPJeAGw0ZA
10.4 Areas and Lengths in Polar Coordinates  http://youtu.be/qHEl7KHOAfE

Chapter 11. Vectors and the Geometry of Space

11.1 Three-Dimensional Coordinate Systems

11.2 Vectors

11.3 The Dot Product

11.4 The Vector or Cross Product

11.5 Equations of Lines and Planes

Chapter 12. Vector Valued Functions

12.1 Vector-Valued Functions and Space Curves    http://youtu.be/0pvywjBjsQw

12.2 Calculus of Vector Functions

12.3 Arc Length and Curvature

*12.4 Motion Along A Space Curve: Velocity and Acceleration

Chapter 13. Partial Derivatives

13.1 Multivariate Functions

13.2 Limits and Continuity of Multivariate Functions

13.3 Partial Derivatives    http://youtu.be/LR89Ct3cEDY

13.4 Differentiability and Total Differentials

13.5 The Chain Rule   http://youtu.be/r3dGYL1vkEU

13.6 Directional Derivatives and Gradient     http://youtu.be/o8L_ShRANjo

13.7 Tangent Plane and Differentiability     http://youtu.be/uOf-5YHKGI4

13.8 Extrema of Multivariate Functions   http://youtu.be/oDZUkOEszOQ

13.9 Lagrange Multiplier

Chapter 14. Multiple Integrals

14.1 Double Integrals     http://youtu.be/jZ2pAmPZYOE

14.2 Double Integrals in Polar Coordinates    http://youtu.be/olQgihl5aZg

14.3 Surface Area     http://youtu.be/p9R0TTLfBzk

14.4 Cylindrical Coordinates and Spherical Coordinates   http://youtu.be/q3FKd2UxV_I

14.5 Triple Integrals    http://youtu.be/r1tzH9Ibbqk

14.6 Triple Integrals in Cylindrical and Spherical Coordinates  http://youtu.be/xd0U4_C2ePY

14.7 Change of Variables in Multiple Integrals  http://youtu.be/INn-bkgXYNg

Chapter 15. Vector Calculus

15.1 Vector Differentiation  http://youtu.be/q0aVmUCXgTI

15.2 Line Integrals   http://youtu.be/wHINlpNXYaU

15.3 Independence of the Path   http://youtu.be/jGGOL3QDj1Y

15.4 Green’s Theorem in Plane  http://youtu.be/WxdTbaSb_ZI

15.5 Curl and Divergence  http://youtu.be/IswmJUCTeNA

15.6 Surface and Area   http://youtu.be/xX6tNVpegbs

15.7 Surface Integrals  http://youtu.be/nrzIrM4doLo

15.8 Stokes’ Theorem   http://youtu.be/t4skc_PzJvg

15.9 Divergence Theorem  http://youtu.be/3BmcFr81kuQ

SKKU 선형대수학 Jordan 표준형, SGLee  : http://youtu.be/Dn4qBxgUJcA

< 후에 추가할 부분 >

미적분학 with Sage Sec-5-4 Net Change Theorem, Problem, 문제풀이 by

미적분학 with Sage Sec 8.3 Center of Mass

미적분학 with Sage Sec *8.4 Differential equations

• 미적분학 with Sage Sec-11.3 The Dot Product

• 미적분학 with Sage Sec-11.4 The Vector or Cross Product

미적분학 with Sage Sec-11.6 Cylinders and Quadric Surfaces

(미적분학 with Sage Sec-12.3 Arc Length and Curvature
(미적분학 with Sage Sec-12.4 Motion Along A Space Curve: Velocity and Acceleration

(미적분학 with Sage Sec-13.2 Limits and Continuity of Multivariate Functions, 문제풀이 by 김건호

(미적분학 with Sage Sec-14.3 Surface Area, 문제풀이 by 이한울

(미적분학 with Sage Sec-15.8 Stokes’ Theorem, 문제풀이 by 이인행

•

각절의 제일 뒤 연습문제의 문제 바로 앞에 (왼쪽) 문제 및 답과 공학도구의 주소

Calculus-Sec-1-1 Functions and Graph   Sec-1-1-Solution-Sage

Calculus-Sec-1-2 Symmetry http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-1-2.htm   Sec-1-2 Symmetry

Calculus-Sec-1-3    Sec-1-3 Solution

Calculus-Sec-1-4 http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-1-4.htm   Sec-1-4 Solution

Sec-2-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-2-1-Sol.htm

Sec-2-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-2-2-Sol.htm

Sec-3-1 Solution

Sec-3-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-3-2-Sol.htm

Sec-3-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-3-3-Sol.htm

Sec-3-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-3-4-Sol.htm

Sec-4-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-4-1-Sol.htm

Sec-4-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-4-2-Sol.htm

Sec-4-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-4-3-Sol.htm

Sec-4-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-4-4-Sol.htm

Sec-4-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-4-5-Sol.htm

Sec-5-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-1-Sol.htm

Sec-5-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-2-Sol.htm

Sec-5-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-3-Sol.htm

Sec-5-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-4-Sol.htm

Sec-5-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-5-Sol.htm

Sec-5-6 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-5-6-Sol.htm

Sec-6-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-6-1-Sol.htm

Sec-6-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-6-2-Sol.htm

Sec-6-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-6-3-Sol.htm

Sec-6-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-6-4-Sol.htm

Sec-6-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-6-5-Sol.htm

Sec-7-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-1-Sol.htm

Sec-7-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-2-Sol.htm

Sec-7-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-3-Sol.htm

Sec-7-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-4-Sol.htm

Sec-7-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-7-Sol.htm

Sec-7-6 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-7-6-Sol.htm

Sec-8-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-8-1-Sol.htm

Sec-8-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-8-2-Sol.htm

Sec-8-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-8-3-Sol.htm

Sec-8-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-8-4-Sol.htm

Sec-9-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-9-1-Sol.htm

Sec-9-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-9-2-Sol.htm

Sec-9-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-9-3-Sol.htm

Sec-9-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-9-4-Sol.htm

Sec-9-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-9-5-Sol.htm

Sec-10-1 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-10-1-Sol.htm

Sec-10-2 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-10-2-Sol.htm

Sec-10-3 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-10-3-Sol.htm

Sec-10-4 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-10-10-Sol.htm

Sec-10-5 Solution http://matrix.skku.ac.kr/Cal-Book/part1/CS-Sec-10-5-Sol.htm

Sec-11-1 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-1-Sol.htm

Sec-11-2 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-2-Sol.htm

Sec-11-3 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-3-Sol.htm

Sec-11-4 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-4-Sol.htm

Sec-11-5 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-5-Sol.htm

Sec-11-6 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-11-6-Sol.htm

Sec-12-1 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-12-1-Sol.htm

Sec-12-2 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-12-2-Sol.htm

Sec-12-3 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-12-3-Sol.htm

Sec-12-4 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-12-4-Sol.htm

Sec-13-1 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-1-Sol.htm

Sec-13-2 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-2-Sol.htm

Sec-13-3 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-3-Sol.htm

Sec-13-4 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-13-Sol.htm

Sec-13-5 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-13-Sol.htm

Sec-13-6 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-6-Sol.htm

Sec-13-7 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-7-Sol.htm

Sec-13-8 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-8-Sol.htm

Sec-13-9 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-13-9-Sol.htm

Sec-14-1 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-1-Sol.htm

Sec-14-2 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-2-Sol.htm

Sec-14-3 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-3-Sol.htm

Sec-14-4 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-4-Sol.htm

Sec-14-5 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-5-Sol.htm

Sec-14-6 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-6-Sol.htm

Sec-14-7 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-14-7-Sol.htm

Sec-15-1 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-1-Sol.htm

Sec-15-2 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-2-Sol.htm

Sec-15-3 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-3-Sol.htm

Sec-15-4 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-4-Sol.htm

Sec-15-5 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-5-Sol.htm

Sec-15-6 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-6-Sol.htm

Sec-15-7 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-7-Sol.htm

Sec-15-8 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-8-Sol.htm

Sec-15-9 Solution http://matrix.skku.ac.kr/Cal-Book/part2/CS-Sec-15-9-Sol.htm

• http://matrix.skku.ac.kr/cal-lab/sage-grapher-inverse.html
1. Newton's method
2. http://matrix.skku.ac.kr/cal-lab/sage-grapher-derivatives.html
3. http://matrix.skku.ac.kr/cal-lab/sage-grapher-integral2.html
4. http://matrix.skku.ac.kr/cal-lab/SKKU-Cell-Matrix-Calculator.html

<Math and Art with Sage>
수학 위에 과학과 예술이~~ : http://matrix.skku.ac.kr/2013-album/Mini-bridge.html

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