IB Math AI AHL 5.18 - Solutions of Second-Order Differential Equations

IB Math AI Unit 5 - Calculus Slidedeck bundle

**IB Math AI & HL Calculus Slide Deck Bundle – Complete Topic 5: Calculus Collection** **Topics:** Limits, Derivatives, Power Rule, Tangents and Normals, Anti-Differentiation, Local Maxima & Minima, Optimisation, The Trapezoidal Rule, Kinematics, Models of Differential Equations, Slope Fields, Numerical Methods, Phase Portraits, and Second-Order Differential Equations. **Level:** IB Mathematics: Applications & Interpretation (SL) and Analysis & Approaches (HL) **File Type:** Complete Editable Slide Deck Bundle **Bundle Price:** £40 (26% discount from individual purchases) --- ### **Overview** This comprehensive bundle covers **every subtopic of the IB Mathematics Calculus syllabus** for both **SL and HL**, providing a fully scaffolded sequence of **editable, classroom-ready slide decks**. Each lesson builds conceptual understanding while reinforcing analytical fluency through worked examples, visual explanations, and real-world applications. Whether you are introducing the derivative for the first time, modeling motion with kinematics, or analyzing eigenvalues in differential systems, this collection delivers the entire calculus pathway—from foundational ideas to advanced applications—ready for immediate classroom use. --- ### **Learning Outcomes** Across this full bundle, students will learn to: * Understand **limits** as the foundation of differentiation. * Apply **differentiation rules** including the power, product, quotient, and chain rules. * Use derivatives to determine **tangents, normals, increasing/decreasing intervals, and turning points**. * Solve **optimization problems** in applied contexts. * Understand **anti-differentiation** and use it to compute areas under curves. * Apply **definite integration** to real-world scenarios including motion and growth. * Use **numerical methods** such as the trapezoidal rule and Euler’s method for approximations. * Model dynamic systems using **differential equations** and **phase portraits**. * Analyze **second-order systems** using eigenvalues, eigenvectors, and physical interpretations. --- ### **What’s Included** * **18 complete PowerPoint lessons** covering all SL and HL calculus subtopics. * Fully editable for classroom customization or digital delivery. * Step-by-step worked examples with complete solutions. * Visual aids, graphs, and diagrams for conceptual reinforcement. * Exercises and review problems aligned with IB-style questioning. * Real-world applications across motion, growth, optimization, and modeling. * Covers all **Applications & Interpretation (SL)** and **Analysis & Approaches (HL)** objectives. --- ### **Topics Covered** #### *Standard Level (AI SL)* * 5.1 **Limits** – Introduction to the concept of limits and the definition of the derivative. * 5.2 **Increasing & Decreasing Functions** – Using first derivatives to describe function behavior. * 5.3 **The Power Rule** – Fundamental rule of differentiation for polynomial functions. * 5.4 **Tangents & Normals** – Finding equations of lines to a curve using derivatives. * 5.5 **Anti-Differentiation** – The reverse of differentiation and area interpretation. * 5.6 **Local Maxima & Minima** – Classifying turning points using first and second derivatives. * 5.7 **Optimisation in Context** – Real-world problems requiring maximum or minimum values. * 5.8 **The Trapezoidal Rule** – Numerical approximation of areas under a curve. #### *Higher Level (AI/AA HL)* * 5.9 **More Derivative Rules** – Product, quotient, and chain rules; related rates. * 5.10 **The Second Derivative** – Concavity, curvature, and point classification. * 5.11 **Indefinite Integrals** – Integration as the inverse of differentiation. * 5.12 **Volumes of Revolution** – Calculating volumes using integration. * 5.13 **Kinematics** – Modeling motion using differentiation and integration. * 5.14 **Models of Differential Equations** – Solving growth and decay models by separation of variables. * 5.15 **Slope Fields** – Graphical representations of differential equations. * 5.16 **Numerical Solutions of Differential Equations** – Euler’s method and approximations. * 5.17 **Phase Portraits of Coupled Differential Equations** – Eigenvalues, stability, and trajectory analysis. * 5.18 **Solutions of Second-Order Differential Equations** – Analytical and numerical solutions with applications. --- ### **Why You’ll Love It** * Comprehensive coverage of every **IB Calculus subtopic**, all in one resource. * Perfectly sequenced to follow the **IB syllabus structure** for both SL and HL. * Fully editable and adaptable for **in-person or online instruction**. * Professionally designed, visually clear, and pedagogically consistent. * Excellent value—save **26% (£14)** when purchasing as a complete bundle. * A complete calculus teaching solution—no additional resources required. --- ### **Tags** IB Math AI, IB Math HL, Calculus, Differentiation, Integration, Differential Equations, Optimization, Kinematics, Limits, Tangents, Trapezoidal Rule, Numerical Methods, Phase Portraits, IB Curriculum, Lesson Slides, Bundle, Teaching Resources, IB Mathematics