Chapter 2 Theorem 2.2 (w/o proof) Definition 2.4 Knowledge of simple RK methods (Euler, trapezoidal) Definition of order Lemma 2.5 (proof) Lemma 2.6 (proof) Concept of autonomization and Lemma 2.7 (w/o proof) Rooted trees Theorem 2.12 (w/o proof) Theorem 2.16 (proof idea) Chapter 3 Theorems 3.2 + 3.3 (w/o proof) Absolute stability, stability domain Definition 3.7 Theorem 3.8 (w/o proof) Lemma 3.9 (proof) Algorithm (3.16) Examples of implicit RK (implicit Euler, implicit midpoint rule) Why are Rosenbrock methods important? Chapter 4 Theorem 4.1 (proof) Theorem 4.2 (proof) Theorem 4.3 (w/o proof) Understand the gaps between necessity and sufficiency for second-order conditions descent direction Armijo rule (4.5) Lemma 4.6 (w/o proof) Algorithm 4.7 Theorem 4.11 (w/o proof) Theorem 4.12 (first part of proof, 1. and 2.) Theorem 4.13 (w/o proof) BFGS Idea of nonlinear CG (Algorithm 4.16) Definition 4.18 Lemma 4.19 (proof) Definition 4.21 Lemma 4.22 (idea of proof) Idea of Algorithm 4.24 Theorem 4.26 (w/o proof) Algorithm 4.28 Theorem 4.29 (w/o proof) Chapter 5 Definition 5.4 Theorem 5.5 (proof) Definition 5.8 Theorem 5.11 (precise statement + full proof, w/o proof of Farkas) Theorem 5.12 (w/o proof) Solution of QP (5.21) Lemma 5.13 (w/o proof) Algorithm 5.1 Idea of IP methods; derivation of (5.31) Definition 5.16 Theorem 5.17 (proof) Lemma 5.20 1, 4, + (5.45) (w/o proof) Lemma 5.21 (proof) (5.49) + optimal choice of alpha for strongly convex, smooth f