Maths for Physicists
55 videos • 16,177 views • by Mark Ancliff
These are videos for an introductory maths course for physics students at the Catholic University of Korea.
1
1(a) Introduction to differentiation
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2
1(b) Proofs of basic derivatives
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3
1(c) Derivatives: Basic properties
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4
1(d) Calculating derivatives: examples
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5
2a) Applications of differentiation
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6
2b) Newton-Rhapson method: Examples
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7
2c) Second derivative test: Examples
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8
3a) Introduction to Taylor Series
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9
3b) Derivation of 5 basic Taylor Series
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10
3c) Taylor Series: Examples
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11
3d) Applications of Taylor Series
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12
4a) Introduction to integration
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13
4b) The definite integral and the Fundamental Theorem of Calculus
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14
4c) Integration by substitution: Examples
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15
4d) Integration by parts: Examples
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16
4e) Integration by partial fractions: Examples
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17
5a) Introduction to complex numbers
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18
5b) Complex number arithmetic
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5c) The complex exponential
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5d) More functions of complex numbers
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21
5e) Calculations with complex numbers: Examples
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22
6a) Introduction to vectors
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23
6b) The scalar product
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6c) The vector product
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25
6d) Lines and planes
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6e) Distances between points, lines and planes
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27
6f) Intersections of lines and planes
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28
6g) Proof of scalar and vector product formulas
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29
6h) An interesting property of the scalar and vector products
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30
7a) Introduction to linear transformations
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31
7b) Matrices
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32
7c) Multiplying matrices
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7d) Inverse matrices (in 2D)
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7e) Properties of the determinant
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35
8a) Introduction: the matrix of determinants
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36
8b) Finding the determinant
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37
8c) Determinants: a useful theorem and examples
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38
8d) Finding the inverse matrix
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39
8e) Special matrices
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40
8f) Geometrical interpretation of the determinant
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41
8g) Invariance of vector and scalar products under rotation of basis
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42
9a) Introduction to Eigenvectors and Eigenvalues
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43
9b) How to find Eigenvectors and Eigenvalues
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44
9c) Finding Eigenvectors and Eigenvalues: Examples
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45
9d) The Diagonalization Formula
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46
9e) Using the Diagonalization Formula
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47
9f) When can (can't) you diagonalize?
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48
9g) Diagonalization of Special Matrices (Proof)
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49
10a) Calculus in Higher Dimensions: Introduction
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50
10b) Taylor Series in higher dimensions
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51
10c) Taylor Series: Examples
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52
10d) Second derivative test in 2D
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53
10e) Second derivative test: Example
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54
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55
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