Add Phase 1 content: Elliptic PDEs, Burgers, and Shallow Water Equations

New chapters and sections:
- Chapter 6: Elliptic PDEs and Iterative Solvers (Laplace, Poisson)
- Chapter 7: Systems of PDEs (Shallow Water Equations)
- New section in Chapter 5: Burgers Equation

Key Devito patterns introduced:
- Dual-buffer Function pattern for steady-state problems
- Buffer swapping via argument substitution
- TimeFunction pseudo-timestepping for elliptic PDEs
- first_derivative() with explicit fd_order and side parameters
- Multiple coupled TimeFunction objects for PDE systems
- ConditionalDimension for efficient snapshot saving
- Function for static fields (bathymetry)

New solvers: laplace_devito.py, poisson_devito.py, burgers_devito.py, swe_devito.py
New tests: 62 tests (18 elliptic, 21 burgers, 23 swe)
Added Makefile for common build commands

Author: ggorman

.typos.toml

@@ -6,3 +6,5 @@ ue = "ue"
 # Strang splitting (named after mathematician Gilbert Strang)
 strang = "strang"
 Strang = "Strang"
+# Variable name for "p at iteration n" in Jacobi iteration
+pn = "pn"

Makefile

@@ -0,0 +1,70 @@
+# Makefile for Finite Difference Computing with PDEs book
+
+.PHONY: pdf html all preview clean test test-devito test-no-devito lint format check help
+
+# Default target
+all: pdf
+
+# Build targets
+pdf:
+	quarto render --to pdf
+
+html:
+	quarto render --to html
+
+# Build both PDF and HTML
+book:
+	quarto render
+
+# Live preview with hot reload
+preview:
+	quarto preview
+
+# Clean build artifacts
+clean:
+	rm -rf _book/
+	rm -rf .quarto/
+	find . -name "*.aux" -delete
+	find . -name "*.log" -delete
+	find . -name "*.out" -delete
+
+# Test targets
+test:
+	pytest tests/ -v
+
+test-devito:
+	pytest tests/ -v -m devito
+
+test-no-devito:
+	pytest tests/ -v -m "not devito"
+
+test-phase1:
+	pytest tests/test_elliptic_devito.py tests/test_burgers_devito.py tests/test_swe_devito.py -v
+
+# Linting and formatting
+lint:
+	ruff check src/
+
+format:
+	ruff check --fix src/
+	isort src/
+
+check:
+	pre-commit run --all-files
+
+# Help
+help:
+	@echo "Available targets:"
+	@echo "  pdf          - Build PDF (default)"
+	@echo "  html         - Build HTML"
+	@echo "  book         - Build all formats (PDF + HTML)"
+	@echo "  preview      - Live preview with hot reload"
+	@echo "  clean        - Remove build artifacts"
+	@echo "  test         - Run all tests"
+	@echo "  test-devito  - Run only Devito tests"
+	@echo "  test-no-devito - Run tests without Devito"
+	@echo "  test-phase1  - Run Phase 1 tests (elliptic, burgers, swe)"
+	@echo "  lint         - Check code with ruff"
+	@echo "  format       - Auto-format code with ruff and isort"
+	@echo "  check        - Run all pre-commit hooks"
+	@echo "  help         - Show this help message"

_quarto.yml

@@ -19,6 +19,8 @@ book:
         - chapters/diffu/index.qmd
         - chapters/advec/index.qmd
         - chapters/nonlin/index.qmd
+        - chapters/elliptic/index.qmd
+        - chapters/systems/index.qmd
     - part: "Appendices"
       chapters:
         - chapters/appendices/formulas/index.qmd
@@ -169,6 +171,8 @@ src_diffu: "https://github.com/devitocodes/devito_book/tree/devito/src/diffu"
 src_nonlin: "https://github.com/devitocodes/devito_book/tree/devito/src/nonlin"
 src_trunc: "https://github.com/devitocodes/devito_book/tree/devito/src/trunc"
 src_advec: "https://github.com/devitocodes/devito_book/tree/devito/src/advec"
+src_elliptic: "https://github.com/devitocodes/devito_book/tree/devito/src/elliptic"
+src_systems: "https://github.com/devitocodes/devito_book/tree/devito/src/systems"
 src_formulas: "https://github.com/devitocodes/devito_book/tree/devito/src/formulas"
 src_softeng2: "https://github.com/devitocodes/devito_book/tree/devito/src/softeng2"