[SKKU Calculus 미적분학]

 

About this book : 

http://matrix.skku.ac.kr/Cal-Book/      (SGLee)

http://matrix.skku.ac.kr/cal-book1/


Main Author : Sang-Gu Lee


Co-Authors : Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert Beezer, Quoc-Phong Vu, Lois Simon, Suk-Geun Hwang.


Reviewers : Hyunsoo Kim, Jaedong Sim, Insung Hwang, Mohit Kumbhat, L. Shapiro, R. Sakthivel, K. Das,  Victoria Lang,


 


 

 Part I   Single Variable Calculus

 

                                  http://matrix.skku.ac.kr/cal-book1/

 

 Part II  Multivariate Calculus

 

 

미적분학 1 (Math &Coding) 강의 (학생들이 제출한 과제/평가) 기록 :

        http://matrix.skku.ac.kr/Cal-Book1/Calculus-1/ 


미적분학 2 (Math &Coding) 강의 (학생들이 제출한 과제/평가) 기록 :

        http://matrix.skku.ac.kr/Cal-Book1/Calculus-2/ 


in   http://matrix.skku.ac.kr/Cal-Book1/ 

and http://matrix.skku.ac.kr/2019-album/


[동영상 강의]

 

1.1 History of Calculus http://youtu.be/ODfMaHgIhAc 강좌운영소개 http://youtu.be/XWEQFlv4jKc


미적분학의 개념  http://matrix.skku.ac.kr/Calculus-Story/index.htm  

 

Chapter 1. Functions http://matrix.skku.ac.kr/Cal-Book1/Ch1/

강의 : http://youtu.be/cl8GqIWIRD0


문제풀이 by 곽주현 http://youtu.be/BNKUzSohiD8

문제풀이 by 장찬영 http://youtu.be/x0E0ZMxZ3Og

문제풀이 by 임효정 http://youtu.be/vx7GCWY68Zw


Chapter 2. Limits and Continuity      http://matrix.skku.ac.kr/Cal-Book1/Ch2/


2.1 Limits of functions 강의 :  http://youtu.be/VBCeAllP1M0

    문제풀이 by 장재철-이훈정,   http://youtu.be/LZSmRPAAXME

    문제풀이 by 황인철          http://youtu.be/hj8d-j_DGf4


2.2 Continuity            http://youtu.be/zGxx3PUCTnM

    문제풀이 by 이훈정          http://youtu.be/azrkT1RP4-c



Chapter 3. Theory of Differentiation     http://matrix.skku.ac.kr/Cal-Book1/Ch3/


3.1 Definition of Derivatives, Differentiation 강의 :http://youtu.be/A-vDsF9ulTs

        문제풀이 by 김태현  http://youtu.be/7wTBWuk2CzU


3.2 Derivatives of Polynomials, Exponential Functions, Trigonometric Functions, The product rule   http://youtu.be/XXMnCESesfQ

        문제풀이 by 조건우    http://youtu.be/Ei5KGW9vZhE


3.3 The Chain Rule and Inverse Functions  http://youtu.be/HfScHEsPfKI

        문제풀이 by 유휘의   http://youtu.be/aSKm12922FE


3.4 Approximation and Related Rates   http://youtu.be/ViRwEJ0Wfkw

        문제풀이 by 김종민  http://youtu.be/JmBOv6_D6qA

 

Chapter 4. Applications of Differentiation      http://matrix.skku.ac.kr/Cal-Book1/Ch4/


4.1 Extreme values of a function 강의 : http://youtu.be/mXVU8OqIHJY

        문제풀이 by 김태영  http://youtu.be/_V4MryNEzWY


4.2 The Shape of a Graph    http://youtu.be/cZrAF_77On4

        문제풀이 by 김태영 http://youtu.be/SVOWADHlzV8


4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule http://youtu.be/vp-gck5-gKE

        문제풀이 by 신종희   http://youtu.be/gR2luDDPsMY


4.4 Optimization Problems   http://youtu.be/k0NtkmZFnh8

        문제풀이 by 이승철   http://youtu.be/AELEV2ElaeQ


4.5 Newton’s Method  http://youtu.be/VxCfl2JzMYU

        문제풀이 by 이승철  http://youtu.be/fdBHQ46g9RE


Chapter 5. Integrals     http://matrix.skku.ac.kr/Cal-Book1/Ch5/


5.1 Areas and Distances 강의 : http://youtu.be/mT_oxlD6RSA

        문제풀이 by 남택현  http://youtu.be/Y_nCn76RPmY


5.2 The Definite Integral   http://youtu.be/GIm3Oz58Ti8

        문제풀이 by 남택현  http://youtu.be/iUsf1h_hTAE


5.3 The Fundamental Theorem of Calculus   http://youtu.be/Zf1HT2H2fbA

        문제풀이 by 정승찬 & Kim  http://youtu.be/Pa4Z38KkDVY


5.5 The Substitution Rule   http://youtu.be/h7tmvmNOliU

        문제풀이 by 이한울 http://youtu.be/0TMbpCPO4Uc


5.6 The Logarithm Defined as an Integral  http://youtu.be/kD0Z9PqetsA

        문제풀이 by 이한울   http://youtu.be/ymDImdIQ90c


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

 


Chapter 6. Applications of Integration

                    http://matrix.skku.ac.kr/Cal-Book1/Ch6/  


6.1 Areas between Curves 강의 : http://youtu.be/o53phm5cqJE


6.2 Volumes      http://youtu.be/4-ChOAFbJAs

        문제풀이 by 김종민  http://youtu.be/Fd4Mguf2dbU


6.3 Volumes by Cylindrical Shells   http://youtu.be/qM1izf8qeX8

        문제풀이 by 신영찬  http://youtu.be/gNaKkA0UNHg      


6.4 Work         http://youtu.be/u3ZaJWhKy6k

        문제풀이 by 김건호  http://youtu.be/SmIo2yaxNsY


6.5 Average Value of a Function   http://youtu.be/zmEeGmwQTB0

        문제풀이 by 신종희  http://youtu.be/BVahd-DJoe8 



Chapter 7. Techniques of Integration  

                 http://matrix.skku.ac.kr/Cal-Book1/Ch7/  


7.1 Integration by Parts 강의 :  http://youtu.be/WX-6C9tCneE

        문제풀이 by 이인행  http://youtu.be/jKCAGJ4HqvQ


7.2 Trigonometric Integrals   http://youtu.be/sIR0zNGQbus

        문제풀이 by 김태현  http://youtu.be/ytETYf1wLbs


7.3 Trigonometric Substitution   http://youtu.be/avTqiEUi8u8

        문제풀이 by 이훈정  http://youtu.be/utTQHIabTyI 


7.4 Integration of Rational Functions by the Method of Partial Fractions

                  http://youtu.be/KLTHp_7G4cI 

        문제풀이 by 장재철  http://youtu.be/SkNW_bax0YI


7.5 Guidelines for Integration   http://youtu.be/Fgn8U4We60o

        문제풀이 by 김대환    http://youtu.be/-N9Fe_Arp2c


7.6 Integration Using Tables    http://youtu.be/tn9jLkgTMp8

        문제풀이 by 조건우    http://youtu.be/EnEQ9ZS3B_k


7.7 Approximate Integration     http://youtu.be/hg2pw1n1cZI


7.8 Improper Integrals      http://youtu.be/rquxbYrC0Yc

        문제풀이 by 이송섭   http://youtu.be/C3kb4c9nLXM

        문제풀이 by 이인행    http://youtu.be/dfSkjvmSXYo 

 

Chapter 8. Further Applications of Integration

               http://matrix.skku.ac.kr/Cal-Book1/Ch8/  


8.1 Arc Length 강의 :  http://youtu.be/7OVqI20z_Bw

        문제풀이 by 남택현  http://youtu.be/A8N-mDD0ja8


8.2 Area of a Surface of Revolution   http://youtu.be/Eq4i2A8eKxA

        문제풀이 by 정승찬   http://youtu.be/yZFJDJgTJfw


8.3 Applications of Integral Calculus 강의 : http://youtu.be/1ZAJeP16pAQ


8.4 Differential equations 강의 : http://youtu.be/uHfOjz8I4-s


Chapter 9. Infinite Sequences and Infinite Series

                    http://matrix.skku.ac.kr/Cal-Book1/Ch9/  


9.1 Sequences and Series   http://youtu.be/rz8ZS4Y_cvc 

        문제풀이 by 문지호 http://youtu.be/Qo0MArZG2EA

        문제풀이 by 이원준  http://youtu.be/O6y1v5fJA0k  


9.2 Tests for convergence of series with positive terms http://youtu.be/mxwSv6ApZ2g

        문제풀이 by 김범윤   http://youtu.be/1flKAnlv9LA


9.3 Alternating Series and Absolute Convergence  http://youtu.be/NtSitFNv9Mk

        문제풀이 by 계성곤      http://youtu.be/e_5D0dzrqwc  


9.4 Power Series  http://youtu.be/426kkrMArgs

        문제풀이 by 배성준   http://youtu.be/R3AcB12z2kk


9.5 Taylor, Maclaurin, and Binomial Series   http://youtu.be/3zSPSvYHJQI

        문제풀이 by 우시명       http://youtu.be/NSFrYRYZ6Qc

 


Chapter 10. Parametric Equations and Polar Coordinates

                         http://matrix.skku.ac.kr/Cal-Book1/Ch10/ 


10.1 Parametric Equations  동영상 강의:    http://youtu.be/hQGCZk1tpuA

        문제풀이 by 문지호       http://youtu.be/uz1DkKVeD2k

        문제풀이 by 임효정       http://youtu.be/Ybs68e0iMZI  


10.2 Calculus with Parametric Curves   http://youtu.be/QFMSbGKhoX4

        문제풀이 by 장찬영  http://youtu.be/yF5oZOQVnCE


10.3 Polar Coordinates    http://youtu.be/lKPJeAGw0ZA

        문제풀이 by 계성곤  http://youtu.be/smAmDRK-tWY

        문제풀이 by 황인철  http://youtu.be/4hoVKvk8dq0


10.4 Areas and Lengths in Polar Coordinates http://youtu.be/qHEl7KHOAfE 

        문제풀이 by 곽주현 http://youtu.be/LRmasW9uqYY


10.5 Conic Section http://matrix.skku.ac.kr/2014-Album/Quadratic-form/index.htm

        문제풀이 by 변희성    http://youtu.be/ONItxvlsnb8

        문제풀이 by 이한울    http://youtu.be/CZ9SHMtqVy4  


Chapter 11. Vectors and the Geometry of Space

                       http://matrix.skku.ac.kr/Cal-Book1/Ch11/  


11.1 Three-Dimensional Coordinate Systems

        문제풀이 by 김태현  http://youtu.be/_s_2T1VVob8

11.2 Vectors

        문제풀이 by 오교혁  http://youtu.be/BFgh6irMqsc

11.3 The Dot Product

11.4 The Vector or Cross Product

11.5 Equations of Lines and Planes

        문제풀이 by 구본우  http://youtu.be/lxuGE_Erthg

11.6 Cylinders and Quadric Surfaces  


Chapter 12. Vector Valued Functions

          강의록:    http://matrix.skku.ac.kr/Cal-Book1/Ch12/  


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

        문제풀이 by 최양현  http://youtu.be/jvMI6OzdR_I


12.2 Calculus of Vector Functions

        문제풀이 by 김동윤  http://youtu.be/VS5rPyOjP2I


12.3 Arc Length and Curvature

*12.4 Motion Along A Space Curve: Velocity and Acceleration  


Chapter 13. Partial Derivatives

                    http://matrix.skku.ac.kr/Cal-Book1/Ch13/  


13.1 Multivariate Functions

        문제풀이 by 구본우  http://youtu.be/As_0AYApHlM


13.2 Limits and Continuity of Multivariate Functions


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

        문제풀이 by 김동윤            http://youtu.be/rSYLp1mSMXY


13.4 Differentiability and Total Differentials

        문제풀이 by 김범윤  http://youtu.be/qDmCWBiXbIA


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

        문제풀이 by 김유경        http://youtu.be/vzN5By6qzvM


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

        문제풀이 by 김태현     http://youtu.be/2_7TOUuzJoE


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

        문제풀이 by 서용태      http://youtu.be/GDkE8OqUvsk


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

        문제풀이 by 오교혁   http://youtu.be/FWmk_MasIjE


13.9 Lagrange Multiplier    

        문제풀이 by 이원준  http://youtu.be/YMGdQWBzyrI



Chapter 14. Multiple Integrals

                       http://matrix.skku.ac.kr/Cal-Book1/Ch14/   


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

        문제풀이 by 이인행    http://youtu.be/w8g9fgcEP4A


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

        문제풀이 by 이지석   http://youtu.be/jpsObxtZ50A


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


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

        문제풀이 by 최양현     http://youtu.be/F9u6pMubVRs


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

        문제풀이 by 이인행         http://youtu.be/C-uPM3km96k 


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

                     http://matrix.skku.ac.kr/Cal-Book1/Ch15/  


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

        문제풀이 by 김동윤  http://youtu.be/iSUME4Q1WPM


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

        문제풀이 by 김범윤      http://youtu.be/ZdRjCfJeHM8


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

        문제풀이 by 김유경   http://youtu.be/TreCe8ESEiU


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

        문제풀이 by 서용태   http://youtu.be/wLTHYaANwtI


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

        문제풀이 by 오교혁 http://youtu.be/j7F3xVNdHvA


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


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

        문제풀이 by 이원준 http://youtu.be/s_MRgW2By38


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


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

        문제풀이 by 최주영  http://youtu.be/vGMLoGWF1Is

 


[실습실] (New Version) http://matrix.skku.ac.kr/cal-book1/

 

Part I  Single Variable Calculus 

Part II  Multivariate Calculus 

 

       http://matrix.skku.ac.kr/Cal-Book/

       http://matrix.skku.ac.kr/Mobile-Sage-G/sage-grapher.html  

        http://matrix.skku.ac.kr/Calculus-Appendix/

        http://matrix.skku.ac.kr/Calculus-Story/

        http://matrix.skku.ac.kr/Calculus-Map/

        http://matrix.skku.ac.kr/Lab-Book/Sage-Lab-Manual-1.htm

        http://matrix.skku.ac.kr/cal-lab/Math-CAS.htm 


     2014 Midterm Exam of  Calculus (pdf)

     2014 Final Exam of  Calculus (pdf)

     2013 Midterm Exam of  Calculus (pdf)

     2013 Final Exam of  Calculus (pdf)

     2013 Midterm Exam of  Calculus 2 (pdf)

     2013 Final Exam of  Calculus 2 (pdf)


Part I  Single Variable Calculus 

http://matrix.skku.ac.kr/Cal-Book/part1/part1.html

Part II  Multivariate Calculus 

http://matrix.skku.ac.kr/Cal-Book/part2/part2.html 


[Grapher]

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-integral2.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-inverse.html

 http://matrix.skku.ac.kr/cal-lab/cal-Newton-method.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-derivatives.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-integral.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-integral2.html

 http://matrix.skku.ac.kr/cal-lab/SKKU-Cell-Matrix-Calculator.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-butterfly.html
http://matrix.skku.ac.kr/cal-lab/sage-grapher-cochleoid.html
http://matrix.skku.ac.kr/cal-lab/sage-grapher-dewdrop.html
http://matrix.skku.ac.kr/cal-lab/sage-grapher-epicycloid.html (수정필요)
http://matrix.skku.ac.kr/cal-lab/sage-grapher-flower.html

http://matrix.skku.ac.kr/cal-lab/sage-grapher-pinwheel.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Gear-Curve.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Bicorn.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Cartesian-Oval.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Double-Folium.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Figure-Eight-Curve.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Folium.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Involute-of-a-Circle.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Kappa-Curve.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Lame-Curves.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Lituus.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Nephroid.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Pearls-of-Sluze.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Serpentine.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Tricuspoid.html  

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Fermat-Spiral.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Freeth-Nephroid.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Durer-Shell-Curves.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Newton-Diverging-Parabolas.html

 http://matrix.skku.ac.kr/cal-lab/sage-grapher-Talbot-Curve.html


Copyright @ 2020 SKKU Matrix Lab. All rights reserved.
Made by Manager: Prof. 
Sang-Gu Lee and Dr. Jae Hwa Lee  & 김응 기  http://matrix.skku.ac.kr/sglee/ and http://matrix.skku.ac.kr/cal-book/


*This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03035865).