Freshman Journal 1.2.13

A: Real Analysis
Cue from Bartle and Sherbert (2000) Chapters 2, 3, 4 and 5 (corresponding to school notes 1, 2, 4, 5). Chapter 3 (Infinite Series) is sadly not represented in textbook.
Summary:
Chapter 1: ℝ
Chapter 2: Sequences
Chapter 3: Series
Chapter 4: Limits of functions
Chapter 5: Continuous functions
Modus Operandi: Mop up unanswered questions in tutorials (without reference to answers), finish textbook exercises.

B: Engineering Maths II
Cue from Farlow et al. (2007) Chapters 1-6 and 8.
The textbook syllabus is matched to the school notes as follows:
(School notes : Textbook sections)
Part 1. ODE and applications
Chapter 1 ODEs: 1.3, 2.2, 4.2-5
Chapter 2 Oscillations: 4.1, 4.6, 4.7
Chapter 3 Modelling: 1.1, 2.3-5
Chapter 4 Laplace Transform: 8.1-3
Part 2. Linear Algebra and applications
Chapter 5 Matrices: 3.1, 3.3
Chapter 6 Linear Transformations: 5.1-4
Chapter 7 ODE Systems: 6.2, 6.4
Part 3. PDE
Chapter 8 PDEs: refer to Advanced Engineering Math textbook by Kreyzig
Modus Operandi: Finish remaining textbook exercises, start past-year papers, create help-sheet based on compiled summary.

C: Engineering Physics II
Broad subtopics covered in First-year Engineering Physics, NUS:
1) Classical Mechanics (PC1431)
2) Thermodynamics (PC1431)
3) Electromagnetism
4) Optics
5) Quantum Mechanics
6) Atomic Physics
Modus Operandi: One-page summary per field + detailed overview of derivations (although to derive all that stuff in 4) or 5) is a bit trying)

D: Electrical Engineering
It turns out the content is really quite sparse and can be taken down to one page per chapter. Modus Operandi: copy everything down to a pocket-size (A6) notebook, then read on the bus.

E: German Language
A scheme of organising new vocabulary in the process of being perfected:
1. Nouns (organise into feminine / masculine / neuter)
1.i. by categories: ideas / things/ quantities and events / people / places
1.ii. by verb endings -ung / -eit / -ion / -ie / -ik (all with plural -en; female only)
1.iii. By gender-specific subcategory: e.g. [quantities], [days], [languages]
1.iv. By etymology: I use only [International] for nouns
1.v. By plural forms: e.g. ["-e], [e], [n]
1.vi. By composite roots: e.g. [-tasche(n)], [-pl(ä)tz(e)]

2. Verbs
2.i. Category 1: Modal (e.g. wollen, können, müssen)
2.ii. Category 2: Simple native (e.g. essen, schlafen)
2.iii. Category 3: Compound native (e.g. be.zahlen, ver.kaufen)
2.iv. Category 4: Cognate - native with English correspondent (e.g. trinken)
2.v. Category 5: International - Romance etymologies (e.g. notieren)
2.vi. Category 6: Separable (e.g. vorbei/gehen, wieder/sehen)
"." and "/" are used for clarity.

3. Prepositions
3.i. Accusative prepositions (e.g. bis, durch, entlang)
3.ii. Dative prepositions (e.g. aus, bei, mit)
3.iii. Variable-case prepositions (e.g. an, in, auf)
* note some prepositions can/must come after instead of before its subject

4. Others (these are not subdivided further)
4.i. Conjunctions
4.ii. Adjectives
4.iii. Adverbs