15.2 Logs & Exponentials 2. Exponentials & Base e - Higher Maths Lessons - @MrThomasMaths SQA 'e'

Here is Higher Maths Chapter 15 – Logs & Exponentials Lesson 2 of 9: Exponentials and Base ‘e’ I am using a mix of mainly the Heinemann and Maths in Action Higher textbooks throughout the course. For a few lessons I also dive into the TJ book. A special thanks must go to Grace, Ryan and Connor for kindly providing me with a unique musical intro… 123 videos have now been uploaded to guide you through Higher Maths 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. Straight Line 2. Recurrence Relations 3. Functions 4. Graph Transformations 5. Trig Graphs & Equations 6. Differentiation 7. Polynomials 8. Quadratics 9. Integration 10. Circles 11. Double Angle & Addition Formulae 12. Wave Function 13. Vectors 14. Further Calculus 15. Logs and Exponentials LESSONS 1. STRAIGHT LINE 1.1. Revision of Gradient 1.2. Collinearity 1.3. Gradient = Tan θ 1.4. The Distance Formula 1.5. ax + by + c = 0 1.6. y - b = m(x - a) 1.7. Perpendicular Lines 1.8. Midpoints 1.9. Medians 1.10. Altitudes 1.11. Perpendicular Bisectors 1.12. Points of Intersection 1.13. Chapter Review 2. RECURRENCE RELATIONS 2.1. nth Term & Recurrence Relations Introduction 2.2. Worded Recurrence Relations 2.3. Limits 2.4. Finding A and B 2.5. Chapter Review 3. FUNCTIONS 3.1. Recap, Domain & Range 3.2. Notation & Graphs of Functions 3.3. Composite Functions 3.4. Inverse Functions 3.5. Graphs of Inverse Functions 3.6. Exponential & Logarithmic 3.7. Chapter Review 4. GRAPH TRANSFORMATIONS 4.1. Shapes of Graphs 4.2. y = f(x) ± a 4.3. y = f(x ± a) 4.4. y = -f(x) 4.5. y = f(-x) 4.6. y = kf(x) 4.7. y = f(kx) 4.8. Composite Functions 4.9. Log & Exponential 4.10. Chapter Review 5. TRIG GRAPHS & EQUATIONS 5.1. Radians 5.2. Exact Values 5.3. Trig Graphs - Period & Amplitude 5.4. Trig Graphs - Max / Min 5.5. Solving Trig Equations 1 - Basic & Multiple Angles 5.6. Solving Trig Equations 2 - Squared and Factorising 5.7. Solving Trig Equations 3 - Phase Angle 5.8. Chapter Review 6. DIFFERENTIATION 6.1. Introduction: Notation & Basic 6.2. Indices Revision 6.3. Fractional & Negative Indices 6.4. Further Differentiation 6.5. Gradient of a Tangent / Curve 6.6. Increasing & Decreasing Functions 6.7. Stationary Points & their Nature 6.8. Curve Sketching 6.9. Max & Min in a Closed Interval 6.10. Optimisation 6.11. Displacement, Velocity & Acceleration 6.12. Sketching the Derivative 6.13. Chapter Review 7. POLYNOMIALS 7.1. Introduction & Previous Knowledge 7.2. Nested Form 7.3. Synthetic Division 7.4. Factor Theorem 7.5. Solving Equations / Roots 7.6. Missing Coefficients 7.7. Functions from Graphs 7.8. Curve Sketching 7.9. Chapter Review 8. QUADRATICS 8.1. Sketching a Parabola 8.2. Completing the Square 8.3. Max and Min Values 8.4. Solving Equations 8.5. Solving Inequations 8.6. The Discriminant 8.7. Tangents to a Curve 8.8. Chapter Review 9. INTEGRATION 9.1. Introduction 9.2. Solving Differential Equations (Finding C) 9.3. Definite Integrals (Area Under a Curve) 9.4. Areas Above & Below the x-axis. 9.5. Area Between 2 Curves 9.6. Chapter Review 10. CIRCLES 10.1. x2 + y2 = r2 10.2. (x - a)2 + (y - b)2 = r2 10.3. x2 + y2 + 2gx + 2fy + c = 0 10.4. Equation of a Tangent 10.5. Intersection of a Line and a Circle 10.6. Chapter Review 11. DOUBLE ANGLE & ADDITION FORMULAE 11.1. Cos(A ± B) 11.2. Sin(A ± B) 11.3. Applications of Addition Formulae (Harder Problems) 11.4. Sin 2A & Cos 2A 11.5. Trig Equations involving Double Angles 11.6. Chapter Review 12. WAVE FUNCTION 12.1. kcos(x - α) 12.2. Other Forms 12.3. Multiple Angles 12.4. Max & Min Values 12.5. Solving Trig Equations 12.6. Chapter Review 13. VECTORS 13.1. Recap from National 5 13.2. Unit Vectors 13.3. Parallel Vectors 13.4. Collinearity 13.5. Section Formula 13.6. Vector Diagrams 13.7. The Scalar Product 13.8. The Angle Between Two Vectors 13.9. Properties of the Scalar Product 13.10. Chapter Review 14. FURTHER CALCULUS 14.1. Differentiating Sinx and Cosx 14.2. The Chain Rule 14.3. The Chain Rule with Trig. 14.4. Further Integration 14.5. Integrating Sinx and Cosx 14.6. Integrating Sin(ax + b) & Cos(ax + b) 14.7. Chapter Review 15. LOGS & EXPONENTIALS 15.1. Surds & Indices Recap 15.2. Exponentials & 'e' 15.3. Logarithms 15.4. Log Rules 15.5. Solving Log Equations 15.6. Natural Logs (ln) 15.7. Experimental Data 15.8. Sketching Log Graphs 15.9. Chapter Review