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Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

Part 1 Introduction to discrete dynamical systems. Biology and Dynamics. Growth - Models of Malaria. Maintenance - Models of Neurons. Replication - Models of Genetics. Types of Dynamical Systems. Updating Functions - Describing Growth. A Model Population - Bacterial Growth. A Model Organism - A Growing Tree. Functions - Terminology and Graphs. Exercises. Units and Dimensions. Converting Between Units. Translating Between Dimensions. Checking - Dimensions and Estimation. Linear Functions and Their Graphs. Proportional Relations. The Equation of a Line. Finding Equations and Graphing Lines. Inverse Functions - Looking Backward. Finding Solutions - Describing the Dynamics. Bacterial Population Growth. Solving for Tree Height. Composition of Functions. Solutions and Exponential Functions. Bacterial Population Growth in General. Laws of Exponents and Logs. Expressing Results with Exponentials. Power Functions and Allometry. Power Relations and Exponential Growth. Power Relations and Lines. Power Relations in Biology - Shape and Flight. Oscillations and Trigonometry. Sine and Cosine - A Review. Describing Oscillations with the Cosine. More Complicated Shapes. Modelling and Cobwebbing. A Model of the Lungs. The Lung Updating Function. Cobwebbing - A Graphical Solution Technique. Exercises. Equilibria. Equilibria - Graphical Approach. Equilibria - Algebraic Approach. Equilibria - Algebra Involving Parameters. Nonlinear Dynamics. A Model of Selection. The General Case and Equilibria. Stable and Unstable Equilibria. Simple Heart. Second-Degree Block. The Wenckebach Phenomenon. Part 2 Limits and derivatives. Differential Equations. Bacterial Growth Re-Measured. Rates of Change. The Limit. Limits. Limits of Functions. Applying the Mathematical Definition of a Limit. Properties of Limits. More Limits. Left and Right-Hand Limits. Infinite Limits. Functions with More Complicated Limits. Exercises. Continuity. Continuous Functions. Properties of Continuous Functions. Input and Output Tolerances. Computing Derivatives. The Derivative in General. Linear and Quadratic Derivatives. Derivatives and Graphs. Derivatives of Sums and Products. Derivatives of Sums. Derivatives of Products. Special Causes and Examples. Derivatives of Powers and Quotients. Derivatives of Power Functions. The Quotient Rule. The Power Rule - Negative Powers. Derivatives of Special Functions. The Derivative of the Exponential Function. The Derivative of the Natural Logarithm. The Derivatives of Trigonometric Functions. The Chain Rule. The Derivative of a Composite Function. Derivatives of Inverse Functions. Application of the Chain Rule. Part 3 Applications of derivatives and dynamical systems. Approximating Functions.