4.6 Differential Equations 6: First Order 2 - Particular Solution – Advanced Higher Maths Lessons смотреть онлайн

Here is Advanced Higher Maths, Chapter 4 – Differential Equations
Lesson 6 of 12: First Order Differential Equations - Particular Solution

A special thanks to Grace, Ryan and Connor for kindly providing me with a unique musical intro…

130 videos have now been uploaded to guide you through the Advanced Higher Maths course and each video includes an explanation along with plenty of worked examples to help you gain a solid understanding. Here is a list of both the chapters and the individual lessons to allow you to target specific outcomes.

Enjoy!

CHAPTERS
1. Partial Fractions
2. Differentiation
3. Integration
4. Differential Equations
5. Binomial Theorem
6. Sequences & Series
7. Proof by Induction
8. Functions & Graphs
9. Applications of Calculus
10. Gaussian Elimination & Matrices
11. Vectors
12. Complex Numbers
13. Euclidean Algorithm
14. Proofs

LESSONS

1. PARTIAL FRACTIONS
1. PF1: Distinct Linear Factors
2. PF2: Repeated Linear Factors
3. PF3: Irreducible Quadratic
4. Algebraic Long Division
5. Improper Rational Functions

2. DIFFERENTIATION
1. From First Principles
2. Product Rule
3. Quotient Rule
4. Trig. Terms
5. ‘e’
6. Ln(x)
7. Higher Derivatives
8. Inverse Trig. Functions
9. Implicit Diff 1
10. Implicit Diff 2: Equation of a Tangent
11. Implicit Diff 3: Second Derivatives
12. Logarithmic Diff
13. Parametric Diff 1
14. Parametric Diff 2: Eqn of a Tangent
15. Parametric Diff 3: Second Derivatives
16. Parametric Diff 4: Objects in Motion

3. INTEGRATION
1. Standard Integrals
2. ex
3. Ln(x)
4. Trig. Functions
5. Int by Sub 1
6. Int by Sub 2: Fractions
7. Int by Sub 3: Manipulation
8. Int by Sub 4: Definite Integrals
9. Int by Sub 5: √(a^2- x^2 )
10. Int by Sub 6: Substitution Not Given
11. Inverse Trig. Functions
12. Int using Partial Fractions 1
13. Int using Partial Fractions 2: Algebraic Long Division
14. Int by Parts 1
15. Int by Parts 2: Harder Examples

4. DIFFERENTIAL EQUATIONS
1. Sep the Variables 1
2. Sep the Variables 2: Using Logs and Exponentials
3. Sep the Variables 3: The Particular Solution
4. Sep the Variables 4: Mathematical Models
5. 1st Order Diff Eqn 1
6. 1st Order Diff Eqn 2: The Particular Solution
7. 2nd Order Diff Eqn 1: Homogeneous
8. 2nd Order Diff Eqn 2: Homogeneous – The Particular Solution
9. 2nd Order Diff Eqn 3: Non-Homogeneous
10. 2nd Order Diff Eqn 4: Non-Homogeneous – The Particular Solution
11. 2nd Order Diff Eqn 5: Amended Particular Integral

5. BINOMIAL THEOREM
1. Factorials
2. Binomial Coefficients
3. Binomial Theorem / Expanding (x + y)n
4. Finding Coefficients

6. SEQUENCES & SERIES
1. Sigma Notation
2. The Sum of a Series with Partial Fractions
3. The Method of Differences
4. Summation Formulae
5. Arithmetic Sequences
6. The Sum of an Arithmetic Sequence
7. Geometric Sequences
8. The Sum of a Geometric Sequence
9. Sum to Infinity
10. MacLaurin Series 1
11. MacLaurin Series 2: Harder Examples

7. PROOF BY INDUCTION
1. Standard Examples
2. Harder Examples

8. FUNCTIONS & GRAPHS
1. Sketching Rational Functions
2. Sketching Imp Rational Functions 1
3. Sketching Imp Rational Functions 2 (Stat Points Required)
4. Sketching the Modulus Function
5. Odd and Even Functions
6. Stationary Points Using the Second Derivative
7. Points of Inflection

9. APPLICATIONS OF CALCULUS
1. Displacement, Velocity and Acceleration
2. Related Rates of Change 1 – Exp Defined Rates
3. Related Rates of Change 2 – Imp Defined Rates
4. The Area Between a Curve & the y-axis
5. Volumes of Solids of Revolution 1 X-axis
6. Volumes of Solids of Revolution 2 Y-axis

10. GAUSSIAN ELIMINATION & MATRICES
1. GE 1
2. GE 2 - Special Cases (Redundancy, Inconsistency & Ill-Conditioning)
3. An Introduction to Matrices
4. Matrix Multiplication
5. The Identity Matrix
6. The Determinant of a Square Matrix
7. Inverse of a Matrix
8. Inverse of a 2x2 Matrix
9. Inverse of a 3x3 Matrix
10. Transformation Matrices
11. Composition of Transformations

11. VECTORS
1. Eqn of a Line : Symmetric Form
2. Eqn of a Line : Parametric Form
3. The Intersection of 2 Lines
4. The Angle Between 2 Lines
5. The Eqn of a Plane
6. The Vector Product
7. The Angle Between Two Planes
8. Line & Plane Intersection Point
9. The Angle Between a Line & a Plane
10. The Intersection of Planes
11. The Shortest Dist from a Point to a Line
12. The Shortest Dist from a Point to a Plane

12. COMPLEX NUMBERS
1. Introduction: Add/Subtract/Multiply/Divide
2. Polynomial Equations
3. Polar Form 1: Argand Diagram, Modulus & Argument
4. Polar Form 2: Multiplication & Division
5. De Moivre's Theorem
6. Roots of Complex Numbers
7. Trig. Identities
8. Locus in the Complex Plane

13. EUCLIDEAN ALGORITHM
1. Number Bases (Division Algorithm)
2. EA1: The Greatest Common Divisor
3. EA2: Expressing the GCD in Terms of a and b

14. PROOFS
1. Disproof by Counter Example
2. Direct Proof
3. Negation Statements
4. By Contradiction
5. By Contrapositive