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Integration and differential equations
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Classroom Contents
Mathematics for Finance & Actuarial Studies 2
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- 1 Integrals of trig functions and reduction formulae
- 2 Integration by trig substitution and partial fractions
- 3 Integration + Partial Fractions
- 4 Integration via substitutions.
- 5 Separable Differential Equations
- 6 Linear and Exact Differential Equations
- 7 Homogeneous first order ordinary differential equation
- 8 Mixing problems and differential equations.
- 9 How to solve 2nd order differential equations
- 10 2nd order ODE with constant coefficients: simple method of solution
- 11 2nd order ODE with constant coeffcients: non-standard method of solution
- 12 Solution to a 2nd order, linear homogeneous ODE with repeated roots
- 13 How to solve second order differential equations
- 14 Integration and differential equations
- 15 Sequences and their limits
- 16 What is a Taylor polynomial?
- 17 Limit of a sequence
- 18 Limit of a sequence: L'Hopital's rule applied to $(\ln n)/n$
- 19 Limit of a sequence: $n--$th root of $n^2$
- 20 Intro to series + the integral test
- 21 Series, comparison + ratio tests
- 22 Alternating series and absolute convergence
- 23 What is a Taylor series?
- 24 What is a power series?
- 25 How to calculate power series: a tutorial
- 26 Partial derivatives and error estimation
- 27 Gradient and directional derivative
- 28 Gradient & directional derivative tutorial
- 29 Tangent plane approximation and error estimation
- 30 Tutorial on gradient and tangent plane
- 31 Multivariable Taylor Polynomials
- 32 Taylor polynomials: functions of two variables
- 33 Critical points of functions
- 34 How to find critical points of functions
- 35 Second derivative test: two variables
- 36 Critical points + 2nd derivative test: Multivariable calculus
- 37 How to find and classify critical points of functions
- 38 Max / min on closed, bounded sets
- 39 Lagrange multipliers
- 40 Lagrange multipliers: 2 constraints
- 41 Lagrange multipliers example
- 42 Method of Lagrange multipliers.
- 43 2nd derivative test, max / min and Lagrange multipliers tutorial
- 44 Lagrange multipliers: Extreme values of a function subject to a constraint
- 45 Intro to double integrals
- 46 Double integrals over general regions
- 47 Double integral tutorial
- 48 Double integrals and area
- 49 Double integrals in polar co-ordinates
- 50 Reversing order in double integrals
- 51 Applications of double integrals.
- 52 Double integrals and polar co-ordinates
- 53 Double integrals: reversing the order of integration
- 54 Tutorial on double integrals
- 55 Double integrals: Volume between two surfaces
- 56 Centroid + double integral tutorial
- 57 Double integrals: Volume of a tetrahedron
- 58 Center of mass, double integrals and polar co-ordinates tutorial
- 59 Centroid and double integrals
- 60 Polar coordinates and double integrals
- 61 Reversing order in double integrals
